Back in 2010 and earlier this year we examined multiple features of complex analysis, including the nature of complex numbers, complex functions, simple manipulations - for example, getting a complex number into polar form, as well as complex roots (e.g. Ö2i), the Cauchy -Riemann equations and residue calculus. A basic area includes complex algebra, or solving algebraic problems using the principles of complex numbers. Below are a number of selected problems to challenge math -inclined readers looking for more than Instagram stuff or Trump's idiotic tweets:
1) Let f(z) = ln r + i(q) where r = êz ê and q = Arg(z)
Find f(1)
2)
Find f(2i -3) for f(z) = (z + 3)2(z
– 5i)2
4) Let f(z) = e (-3z)
Find the real and imaginary parts of
the function f(z)
5) Find all solutions for cos (z) = 5
6) Solve for z if: sin z = i sinh 1
Solve for z
8)
Find: f(-3i) for f(z) = (z + 2 – 3i)
¸ (z + 4 – i)
10) Solve: (z + 1)3 = z3
No comments:
Post a Comment