Saturday, March 2, 2013

Solutions, cont'd (3)

(3) We have:

[z3·z4] = (z3·z4) cis(arg(z3) – arg(z4))

We already know: arg(z3) = 14 deg.

And: z3= 4.1 cis(14)

We also saw: z4 = 4 + 3i = 5 cis (36.8)


And: arg(z4) =  36.8  deg

Then write out the product, viz.:


[z3z4] = (z3z4) cis([arg(z3) – arg(z4)] =


[4.1][ 5] cis [arg (14 deg) – arg(36.8 deg)]


For which:


arg(z3) – arg(z4) = [(14) – (36.8)] = -22.8


Therefore:

[z3z4] = 20.5 cis (-22.8) = = 20.5 [(cos (-22.8) + isin(-22.8)]


[z3z4] = 20.5 [(0.92) + i(-0.38)]  = 18.9 - 7.8i   (rounded off )


(Note: The result above corrected from yesterday, since the angular difference in the arguments is (-22.8) not (-24.8)!)

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