math

Question

Question

1) write the following complex number in polar form : Z=(2√3 + 2i)¹⁰/ 1-√3i

2) determine when f(z) = Z+2i / z²-9 is analytic

3) let u(x,y) coshx costy . find an analytic function f(z), such that u = Re(f(z))

4) Solve the equation sinh(2z) = -1.

5) evaluate ln ( 2√3 + 2i ) .

Answer 1

Answer #1

(1. ) Z = (0,13 +21). 1-V3 = (213 +di)? - 1d + tid + 85 i 8+863 (•49--4) ( 213 + )* = (8+803712 = 64-192+120v3i = -188 +128

Answer 2

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