Monday, September 15, 2014

NFL Digs Itself Into A Hole Over Ray Rice and Adrian Peterson

By 'dig itself into a hole' I mean the NFL has been flat out caught in total hypocrisy. This after the jarring images were released of Minnesota Vikings' RB  Adrian Peterson's 4-year old son after being thrashed with a tree branch by his pop. The cuts and wounds so bad that they disclosed an insane fury of a guy totally unhinged taking it all out on his kid (Peterson said he did it because the boy took a video game away from his brother).   Took a video game away? And you thrashed him like the old slave Massahs used to beat their slaves? Give me a break!

Thankfully, Peterson is under indictment for felony assault in Texas as he should be, but meanwhile the NFL and Commissioner Roger Goodell, are perfectly fine with letting this reprobate suit up and play on Sunday. But what about Ray Rice - caught in a video popping his wife and knocking her out? Well.he has been suspended indefinitely.

No one is saying that either of these guys ought to get away with their deeds, but to let Peterson play after he inflicted horrific cuts and welts on a FOUR year old, and not Rice after swatting an adult woman, is beyond the pale. In fact, both need to be suspended and if it's "indefinitely" for Rice, it needs to be in perpetuity for Peterson - with NO chance of reinstatement. The reason is that inflicting massive, deep cuts on a 4 year old (all over) with a sawed off tree branch  is worse than Rice's assault, in my book.

Goodell and his brain trust need to rethink their decisions in each case, and also bear in mind that Peterson faces an actual sentence in TX for his misdeeds, which he's tried to defend using the "spare the rod, spoil the child" bunkum and "my daddy did it to me" crap.

Peterson then, has no business playing this weekend.

Footnote:

As to the question of all those Baltimore fans that showed up with Ray Rice Jerseys on Thursday night, and displaying "unfeeling attitudes",  as many in the media have portrayed it, not so. As wifey- a Ravens' fan - has pointed out: "Those jerseys are damned expensive! They're not going to just toss them at 75 bucks apiece!"

Indeed, and that is a rational reason to wear them though yes, many fans were showing a support for the guy (who as I noted in an earlier post has been a stalwart over the years in the anti-bullying campaigns) and for the team. Also, many of those jerseys (No., 27) were altered to read 'Be NICE' , if any of the assorted critics had paid any attention.

It's time in any case for the NFL to adopt one rule, not several, for any kind of abuse - and not let one miscreant play ball while the other is put in limbo.



Now We Know Fracking Is Making People Sick

Well, many of our fears about fracking have been confirmed as the largest study to date of the link between natural gas drilling and public health shows that those forlorn folks living near fracking sites and relying on well water are more than twice as likely to report skin and respiratory problems. But this shouldn't be news given the hundreds of nasty chemical toxins used in fracking, including toluene, benzene and other carcinogens.

The study, from Yale University and published in the journal Environmental Health Perspectives, surveyed 492 people living in 180 randomly selected households in southwestern Pennsylvania, an area containing more than 600 active natural gas wells. A full 39 percent of those living less than a kilometer (0.6 miles) away from a well, researchers found, said they’d experienced upper respiratory symptoms, including coughing, itchy eyes and nosebleeds, compared to 18 percent living 2 kilometers away or more. And 13 percent of those living close to wells reported skin conditions like persistent rashes and unexplained hair loss, compared to just 3 percent of the others.

The researchers have asserted that they are only reporting on the correlation so they can’t say whether fracking caused these symptoms.   Nor could they be more specific about what mechanism might have been at play. Drawing on past research, they say it’s possible that fracking is contaminating underground wells or causing air pollution, but it could also be that "the symptoms are just being caused by the stress and anxiety associated with living near major drilling operations — or by something else entirely."

This take, however, is hardly plausible given the first hand visual evidence seen, for example, in Josh Fox's Gasland II and the evidence we now have from Colorado investigations revealing that soil, air and ground water have been contaminated. The psychological proximity theory is also bollocks, given all those cases of animals that have died horrific deaths from drinking fracked water - leading their owners to have to send in hundreds of gallons of bottled water for their use too.

Ok, so it’s not a smoking gun and the evidence is primarily anecdotal but it still counts for something.  We also know, predictably, that diehard fracking supporters have been quick to underplay the findings. Enter PR misfit Katie Brown, spokesperson for the pro-drilling Energy in Depth, who asserted after the new results that it’s “just a poll.”

But this is typical dismissive PR reaction such as noted in the terrific anti-PR book by John Stauber and Sheldon Rampton, Toxic Sludge Is Good For You.

In the book, people who have been the recipients of toxic sludge -based fertilizers,  replete with hundreds of chemicals,  were asked about ill effects and they detailed them. However, the PR industry backing the fertilizer manufacturers argued that the people are wrong because it's "just a poll" and besides,  this toxic sludge was great for crops.  Never mind the vomiting, breakouts in rashes and convulsions, which could also be just in their minds. (They saw and smelled the sludge fertilizer and it induced a violent psychological reaction.)

So it's definitely uncanny to behold the parallels to what the pro-fracking PR hacks say here.

The Yale researchers also take care to note that their findings are consistent with earlier studies of these same health symptoms, including those reported by Michelle Bamberger and Robert Oswald. Bamberger, a veterinarian, and Oswald, a professor of molecular medicine at Cornell,  recently explained to Salon that industry secrecy and lax regulations made it difficult to prove a definitive link between fracking and health symptoms. In some states, for example, it's against the law to disclose the content of fracking liquids - though it seems to be ok for a Neoliberal gubernator assholes like John Hickenlooper to drink them to show "they're okay" . It is also against the law in many fracking states for physicians to run tests for the presence of fracking chemicals causing adverse health effects and to disclose them to patients.

Given this Neoliberal foreclosure of evidence, the so-called polls and surveys (such as those made by the Yale researchers in the recent study) assume supreme importance in exposing what these turkeys are doing to us - along with documentaries like Gasland I and II. Let's keep in mind the PR factories will never tolerate the truth, as in the case of anthropogenic global warming, so we must always expect their egregious and reckless counter attacks.

In Pennsylvania, where drilling has exploded in the past six years, whistle-blowers recently accused the state Department of Health of deliberately ignoring health complaints. Critics added that the state has yet to conduct even one study on fracking’s potential health risks.  We want to make sure people know it’s a preliminary study,” lead author Peter Rabinowitz told the New Haven Register, adding, “to me it strongly indicates the need to further investigate the situation and not ignore it.”

But you may be sure these fracking maniacs and their paid off pols won't be put off. They are determined to poison us all for a temporary profit - for energy, fuels likely not even to be used in the U.S. but shipped to China or other places that will pay top dollar.

Despicable! To see the partial list of the chemicals exposed in fracking liquids thanks to the work of those like Colorado Sen. Dianne Dégette, check out the list below:

 Benzene: a powerful bone-marrow poison (aplastic anemia) associated with leukemia, breast and uterine cancer
Keep i
- Styrene, which may cause eye and mucous membrane irritation, neurotoxic effects in the central and peripheral nervous systems.

- Toluene, which may cause muscular incoordination, tremors, hearing loss, dizziness, vertigo, emotional instability and delusions, liver and kidney damage, and anemia.

- Xylene, with cancer-causing (mainly in the kidneys, liver) and neurotoxic effects, as well as reproductive abnormalities.

- Methylene chloride, which may cause cancer, liver and kidney damage, central nervous system disorders and COPD.



Now that this new study is circulating we need to come down even harder on the frackers and that means no longer buying into their codswallop.  They must be made also to conform to the precautionary principle, meaning they must prove fracking is safe - it's not our duty or job to prove it's unsafe!
 

Sunday, September 14, 2014

Longevity Annuities - Are They Really Worth It?

As I noted in previous blog posts, immediate annuities are a financial device that many of us ought to seriously consider in order to ensure a life time stream of income so as not to outlive our money - say stashed in an IRA.  Recall also what the  AARP Bulletin reported in July of 2012. . According to A. Barry Rand ('Financial Capability', p. 38):

"Half of those working have no sense of how much savings they will need in retirement. According to the Center for Retirement Research at Boston College, almost 44% of working households, ages 36 to 62, are at risk of having insufficient savings for their retirement years. This puts even greater pressure on national retirement systems that already face insolvency challenges."

One answer proposed was immediate fixed annuities..

The problem is that getting such an annuity requires turning over a large stash of your money in one lump sum to obtain a monthly income. Right now, for example, checking at the website:


http://www.immediateannuities.com/

One learns that a 55 year old man paying out $100,000 can obtain an immediate fixed annuity for roughly $5,772 a year or $481 a month.

However, we have now learned "longevity policies" are being aggressively touted - that is annuities that don't pay immediately but much later. (Denver Post, Aug. 24, 'Insurance Against Outliving Your IRA'). Typically these start paying out at age 75, when one would receive $24,192 a year. Even better would be waiting until age 85 when you'd receive $81, 936 a year.

But before you begin considering the last, bear in mind the actuarial tables for Social Security which show the typical American at age 55 has only 28.65 years of life expectancy left - and even less for males (about 14.5 years.) So the odds are that despite all the financial hubbub about living to or past 90, the average male will have long since gone quietly into that good night by then. And what happens to the 100 grand you used to purchase the policy? Well, the insurance company keeps your money!

While longevity annuities sound like a terrific idea on the surface, one would be advised to think very carefully before any purchase. In particular, what exact chances do you put on living until 75 (or 85) to collect your big payout? What is your family health history and life expectancy of your parents? If you're not confident in living that long it may be better not to be so greedy and instead take the lesser yearly amounts in a standard immediate annuity. I mean, look, even the standard immediate annuity for the 55 year old will pile up a total of $173, 160 before he could make his first collection at 85 for a longevity version. To me, the odds warrant that choice instead of grabbing for the big $81- odd grand payout and croaking before you get it!

Of course, for normal annuities it is therefore wise to incorporate a death benefit - so if one spouse dies earlier than expected at least the other can get something. Ordinarily this means a drop in the inflation-adjusted income - in the article I cited (Denver Post, ibid.) a drop from 5.9% to 5.4% is cited. What can counterbalance this loss is at least deferring Social Security until age 70.

It also goes without saying, but I will, that to protect your annuity investment you should only go to an insurer with a triple A rating. (Some advisors say 'double A'  should be the limit - but call me cautious!)

As we learn more of how difficult it will be for people in retirement, and the numerous attacks being mounted on Social Security, Americans would be well advised to consider annuities in providing a stream of income in later years - even to supplement their Social Security.

Saturday, September 13, 2014

Is Stephen Hawking Serious About the 'God Particle' Destroying the Universe?

One thing we can say about Stephen Hawking: He's never at a loss to come up with a new way to scare the bejeezus out of complacent humans. Just three years ago he warned of an invasion of advanced aliens that would likely imitate the arrival of the European conquistadors who decimated native peoples in the New World in the 15th-16th centuries. Only this time modern humans would occupy the place of those technologically unsophisticated groups and become fodder for the aliens. It got many people to start thinking that we may have to worry a bit more when we send powerful signals into space - either intentionally or unintentionally.


Most recently, Prof. Hawking has warned that the Higgs boson — or so-called God particle — has the potential to destroy the universe, as reported by the Sunday Times .  This seems even more terrifying than the alien threat because the latter was localized for our own species and corner of the cosmos- as opposed to snuffing the whole 'enchilada'. But when one reads between the lines one quickly realizes Hawking is stretching the bounds of practical scientific prowess and feasibility.

The putative basis of his warning is actually highlighted in more detail in the foreword to the book Starmus, 50 Years of Man in Space.   Therein, the theoretical physicist wrote that if accelerated to high energy levels, the Higgs boson could cause space and time to collapse — and we’d be caught unawares. From the preface:
“The Higgs potential has the worrisome feature that it might become megastable at energies above 100bn giga-electron-volts (GeV). This could mean that the universe could undergo catastrophic vacuum decay, with a bubble of the true vacuum expanding at the speed of light. This could happen at any time and we wouldn’t see it coming.”

However, Hawking is gracious (and sympathetic of human feelings) enough to go on to aver he does not believe that this event will happen in the near future. Gee, thanks a heap, Stevie! But I'd have guessed it anyway given the magnitude of the energy needed from an accelerator (100b GeV) to make that happen. (Let us also bear in mind that the energy scale driving vacuum inflation was last seen just after the Big Bang- whereby the initial cosmos expanded from the size of an atom (about 1 fm in diameter) to several times the radius of the solar system.)

Anyway, Hawking explains for our benefit:

 “A particle accelerator that reaches 100 billion  GeV would be larger than Earth and is unlikely to be funded in the present economic climate.”

Hmmmmmm........"larger than the Earth"...... or more than 8,000 miles long! Yeppers, I believe that would take roughly all the money that's ever been spent on nuclear weapons and their delivery systems - or about 14 trillion dollars (at minimum). So, I don't believe there's anything to fret over, since the energy demands of our population are actually increasing as the reserves are diminishing. (Frackers want you to believe they have the exception but this is mere 'snake oil' to use the parlance of Richard Heinberg)

In point of fact, such energy mastery would be more typical of the Type I Civilization once proposed by Russian cosmologist I.S. Kardashev. By his definition such a civilization would be able to wield and develop energy scales equal to an entire planet's output. (By his reckoning Earth wasn't even at Type 0.1).

(The Higgs boson was theorized by Dr. Peter Higgs in 1964. In 2012, evidence of Higgs boson was discovered by CERN, the European Organization for Nuclear Research. )

All of this interjects the question of what Hawking's next scare is likely to be: a possible collision with a mini-black hole (or one created in the CERN machine?) Or, Earth being blasted by the intense radiation of a gamma burst supernova? I am sure Vegas books will soon be taking bets!

Friday, September 12, 2014

A 'New' Wonder Food - But Can We Get People to Eat It?

Photo: Breadfruit - the wonder food to sace the world?
Food insecurity and hunger is a world wide problem, especially as the global population lurches out of control. I was astounded, for example, to read that currently Africa's population (now 1.1 billion) is expect to comprise 40 percent of the entire global population by 2100. Thus, out of some 15 billion projected by then, some 6 billion will be Africans - as many people as there were in the entire world back in 2001. But how will they eat? What will they eat?

GMO foods, which are currently all the rage as a solution, are not going to be enough, apart from the fact their glyphosate content renders all the foods toxic that they're embedded in. See e.g.
http://brane-space.blogspot.com/2014/03/alzheimers-epidemic-fro-eating-gmo.html

So what other option might there be to halt world hunger, especially in impoverished nations. It turns out that it's the breadfruit, Atcarpus altilis.  Originally brought to the West Indies (Jamaica) by Captain Bligh in 1792, to feed the vast numbers of slaves, the British plantation owners soon learned they weren't accepted. The slaves initially turned their noses up at the lumpy fruit with its potato like texture. 

But fifty years later it had become an island staple and in another fifty years or so a staple in Barbados.  In the island one can see breadfruit trees all over the place. A favorite island dish is "flying fish and breadfruit".  Most often the breadfruit is baked, but I was never able to eat it that way - much too bland. However, when done in the form of pickled breadfruit I could handle it.

The quandary for Barbados, Jamaica and the West Indies - all areas of food insecurity, has been how do you integrate this bland food - which is abundant and indeed thrives in the tropics - into regular menus?

Though bland and the texture potato-ey, there are many benefits. It can be used (as Bajans learned) in both sweet and savory recipes as well as ground into flour.  It's also versatile and surprisingly nutritious (and no need for glyphosates to be added in any GMO form!) It's high in vitamins and minerals, a source of gluten-free carbs and protein and has a higher proportion of essential amino acids than soy. One kilogram breadfruit easily provides the carbs for a family of five for one meal.

Given these benefits it's no surprise than an initiative called "the Alliance to End Hunger" is working toward distributing the fruit to food insecure countries world wide.

This despite the fact the breadfruit has fallen out of favor in Jamaica. (Not yet in Barbados!). So those running the Breadfruit Institute in Hawaii are cognizant of the fact that they need to identify varieties of breadfruit that best suit particular environments, climates and tastes. They understand they can't just foist the fruit on countries in Africa or elsewhere, never mind they have millions of starving people.

Current research at the Breadfruit Institute, according to a New Scientist piece (June 28) is revealing how different varieties compare when one considers things like yield, fruiting season, mineral content and protein. As noted in the article (p. 42):

"The work to identify desirable traits is ongoing. For instance, first indications are that some cultivars may be salt tolerant, important in Caribbean islands where soils are set to get saltier as sea levels rise."

The other problem to be solved before breadfruit can be delivered worldwide is how best to propagate and transport the plants. Eventually, the specialists at BI and elsewhere want to see breadfruit agro-forests in abundance in other food -impoverished nations. First, however, they need to get local people to acquire a taste for it.

Let's hope they succeed!

Thursday, September 11, 2014

Protecting Social Security in Event of Financial Collapse


A recent and critical issue raised by Andrew Biggs in a Wall Street Journal column highlights the large jump in the projections of the Social Security shortfall since 2008. Biggs complains that progressives have responded to the economic collapse by proposing an increase in benefits that would make the shortfall even larger rather than supporting plans for eliminating the projected shortfall. Biggs' focus is exclusively on the solvency of the program, so the actions of progressives can only be understood against the larger economic context.

This is short sighted and absurd.

In fact, an expansion of benefits is a rational response to the economic collapse. Even more so because the collapse was 100 percent preventable and  one of the worst blunders in the history of economic policy-making. Nearly all of it could  have been prevented had two things happened: 1) Preserve the Glass-Steagall Act instead of repealing it in 1999, which allowed commercial banks to engage in investment banking, and 2) Regulate the credit default swaps  - a form of derivative - which took off in 2007-08. These derivatives were responsible for allowing low grade, risky bonds to be rated AAA thereby luring people into them. See e.g.

http://brane-space.blogspot.com/2014/02/lights-go-out-on-dismal-science-long.html

As a result of the credit collapse, many people nearing retirement saw their savings disappear as the stock market collapsed, house prices plummeted and they lost their jobs during their peak savings years. Thus, millions of workers had to draw down their savings to support their families at a point where they had planned to be accumulating wealth for retirement. In addition, due to the weakness of the labor market created by high unemployment, tens of millions of workers have been saddled with stagnant wages over the last six years when they could have expected to see real wage growth in the neighborhood of 1.0 percent annually had the economy continued on the path projected in 2008.

In short, the collapse vastly increased the need for Social Security, which is the basis for the response of progressives such as yours truly  We can't afford to impose any cuts, irrespective of type, because all will create even more financial havoc and economic stress. Biggs is correct that the cost of additional benefits will have to be covered at some point, but there is no obvious reason that it is necessary to come up with the full plan today. Part of the cost can be recovered by increasing the payroll cap as has been proposed by people across the political spectrum.

It is likely that we will need some increase in the payroll tax at some point, but there is little reason that the exact timing needs to be pinned down today. In the decade from 1980 to 1990 the payroll tax increased by over 2.0 percentage points. In spite of this hike, many conservatives tout the eighties as an economic golden age. It is difficult to see why it would be such a disaster if there were a comparable increase somewhere over the next three decades.

Workers care about their after-tax wages which are primarily determined by what they earn before taxes. Due to economic mismanagement and trade and regulatory policies that were designed to redistribute income upward, most workers have seen very little growth in before-tax wages over the last three decades. If they get an even share of the projected growth in compensation over the next three decades, then before tax compensation will be almost 60 percent higher in 2044 than it is today. It is understandable that progressives would be more focused on ensuring that workers get their fair share of economic growth than the risk that 3-4 percent of these gains might be taken back in tax increases to support their retirement.

Beyond Social Security, Medicare must not be cut either! Fix the Debt parasites have vowed  to expand the means testing of Medicare to lower middle income seniors. According to the Newsletter  of the National Committee to Preserve Social Security And Medicare:

"The proposal would shift billions of dollars in additional costs to beneficiaries by further expanding means testing for Medicare Parts B and D – until 25% of all beneficiaries are paying higher, income related premiums. A recent study found that this proposal would eventually impact individuals with annual incomes equivalent to $47,000 in today’s money.”


Let’s make it clear here that $47,000 /yr. is not a princely sum for an annual income, especially for seniors who – unlike younger folks- are burdened by additional health care costs including more medications, as well as the possibility of having to enter a nursing home for everything from a broken hip, to Alzheimers. The nursing homes are not cheap at $3,000 a month or more. Hence, this expanded means testing is nothing short of deplorable. The fact that the richest 1% will still make out like bandits while lower middle income seniors suffer is even more disgusting.


The NCPSSM Newsletter went on to note that this expanded means testing along with a chained CPI for Social Security, and possibly higher eligibility age for Medicare would:


generate a tsunami of seniors living in poverty


Setting the cuts in stark contrast to the wealthy tax payers, the Newsletter goes on:

"The benefit cut resulting from the chained CPI proposal alone would result in Social Security beneficiaries losing about 2 percent of their income, while the 2013 tax increase on wealthy Americans earning $500,000 results in a negligible 0.6 percent loss’


Process that difference! For the half million a year wealthy guy his piddling 0.6% loss is barely equal to the current cost of one share in his favorite hedge funds or a 1/10  kt blood diamond. For the senior it would equal a month's worth of blood pressure and diabetes meds and half his groceries. Do the rich Neoliberals who make up most of the Beltway's blabber set care? Of course not!

In other words, the confluence of benefits cuts is designed to increase inequality and poverty rates dramatically (already 15% of seniors live at or below the poverty line)

By contrast, the increase of Social Security benefits will not only protect it for seniors who need it, but also compensate them for lost wages in the wake of the 2008 meltdown - after which they were unable to get jobs.  Such an increase in Social Security payments can also be justified given how much congress has ransacked over the years - which I enumerate below:

The following data shows how much has been raided each year, the data from the same Trust Fund sources and GAO:

Year:  ................Amount raided

2011.................$67.0 billion

2010.................$87.0 billion

2009...............$137.0 billion

2008...............$180.2 billion

2007...............$186.0 billion

2006...............$185.5 billion

2005..............$173.5 billion

2004..............$151.1 billion

2003.............$155.6 billion

2002.............$159.0 billion

2001.............$163.0 billion

2000.............$151.8 billion
----------------------------

TOTAL:  $2.63 TRILLION

Thus increasing S.S. payments by 10% or so would be an excellent way to start paying that stolen money back to beneficiaries who deserve it.  The worker-to -beneficiary ratio is a red herring meant to deflect attention from the REAL problem which is the yearly raids on monies received from payroll taxes and intended to go to future beneficiaries! So long as these raids continue unabated, NO solution or "re-tooling" of the program will work, not raising payroll taxes, not making cuts, NOTHING!

But providing a significant Social Security increase would at least demonstrate to beneficiaries that their government is operating in good faith with their interests at heart.

An even more important immediate way to do that is to halt the shuttering of Social Security field offices. The Social Security Administration has been forced to close dozens of field offices around the country, thereby limiting access to seniors whose only way may be face-to-face appearance with administrators.   Meanwhile, the Senate Special Committee on Aging held a hearing two months ago after a bipartisan report showed Social Security has closed 64 field offices since 2010, the highest number of closures in a 5-year period in history. (Denver Post, June 19, ‘Agency closes field offices’, p. 18A)
 
Interestingly, as the article also points out (ibid.):

The closings came as applications for retirement and disability benefits are soaring”.

In other words, those who want to kill S.S. via the back door  are adopting the exact same back-handed methods they did with injured vets seeking VA care. In that case, the miserable fuckers declined to approve $24b to expand VA facilities for care – thereby creating the recent crisis we beheld. According to the Post article, again echoing what’s gone on with vets seeking care in the VA system:

Seniors seeking information and help from the agency are facing increasingly long waits, in person and on the phone.”


Blogger R. J. Eskow wrote in June on the Huffington Post that:  “many disabled and elderly Social Security recipients depend on field offices, and the workers in them.” And as Michael Hiltzik of the Los Angeles Times said, “They haven’t been able to cut benefits, so they’re doing the next best thing: making it hard for you to know what you’re due, and harder to get it when it comes due.”

The bottom line is, Americans came together to create the Social Security system to provide a basic, reliable foundation for retirement and disability. Closing field offices and making it more difficult to access benefits information is an attempt to dismantle that foundation.

 

But even before we try to get congress to increase Social Security payments we have to ensure those field offices remain open so that millions of people can access their benefits in the first place! The push to strengthen benefits and enhance them is pointless if the yearly raids on S.S. continue unabated and the Repos keep using budget cuts to shutter S.S. admin offices!

Solutions to Cubic Equation Problems:


 
1) Check that for the roots obtained in the example problem:

a)     (a1 x a2) + (a 2 x a3) + (a3 x a1) = q

AND

b) a1 x a2 x a3 = r

Solution:   From the example problem we saw:

 a1 = 1.103 - 0.665i

a2 = 1.103 + 0.665i

a3 = -1.206

Then: (a1 x a2) = (1.103 - 0.665i) (1.103 + 0.665i ) = 1.659

 
(a 2 x a3)  =   (1.103 + 0.665i) (-1.206)  =  -1.33 – 0.802i

(a3 x a1) =   (-1.206) (1.103 - 0.665i =  -1.33 + 0.802i


So:  (a1 x a2) + (a 2 x a3) + (a3 x a1) =

 
1.659 + (-1.33 – 0.802i) + (-1.33 + 0.802i) »  1.66 – 2.66 =  -1 = q


b) a1 x a2 x a3 = (1.103 - 0.665i) (1.103 + 0.665i)( -1.206) » - 2 = r

 
2) Solve: x3 – 6x2 + 11x – 6

 
Then: p = 6, q = -11, r = 6


 D =  [(- 4p3 r – 27r2 + 18 pqr – 4 q3 + p2 q2)] 1/2


r 1=   - 1/2 + 1/2  Ö- 3

r 2=   - 1/2 -  1/2  Ö- 3


So:  D = 60.033i

x1 = [p3 –9/2 (pq – 3r) – 3/2 x (-3)1/2 x D ]1/3

=  9.085

x2 = (p2 – 3q)/ x1

=   7.595


The roots are then:

a1 = 1/3(p + r2 x x1 + r x x2)   =   7.56


a2 = 1/3( p + r2 x x1+ r x x2)   =  -0.78 – 0.43i


a3 = 1/3( p + r x x1 + rx r2 x x2)

=   -0.78 + 0.43i


Check: a1 + a2 + a3 = p =  6
 

=  7.56 +  (-0.78 – 0.43i)  + ( -0.78 + 0.43i) =  7.56 - 1.56 = 6
 

(a1 x a2) + (a 2 x a3) + (a3 x a1) = q = -11


(a1 – a2) x (a2 – a3) x (a3 – a1) = D = 60.033i

 Q.E.D.