COMPLEX VARIABLES MATC34 ASSIGNMENT 6 . DUE BY OCTOBER 30.
1. Find all singular point, the principal part of the Laurent series and the residue at each of these points
for (a) f = 1+e z , (b) f = z12 221 z , (c) f = z(z21 2 .
2. Find the fo
COMPLEX VARIABLES MATC34. ASSIGNMENT 4 . DUE BY OCTOBER 2.
1. Using Cauchy inequalities for derivatives of analytic function verify the following statement. Let f (z)
be entire function. Assume that |f (z)| |z|+1 for any z. Then the function f (z) is line
COMPLEX VARIABLES MATC34 ASSIGNMENT 1 . DUE BY SEPTEMBER 20.
1. Calculate (1 + i 3)3 straightforward and also with help of polar form.
2. Find all roots 1 5 , (4 + 3i) 5
3. Explain why the inequality |z1 z2 | |z1 | |z2 | is valid for any complex numbe