Complex Analysis Answers

How many angles are found in between 0 and 2π that satisfy the equation ItanxI = 5 ?

Find (z)*2020/3 if z=cos11π/6 +isin7π/6.

Solve the equation (a) z 4 = 24i − 7, (b) z 2 + z −2 = i, (c) z 6 = (1 + z) 6 

Let z1 =-i/1+i,z2 = 1+i/1-i,and z3 = 1/10[2(i-1)1 +(i +√3)³+(1- i)(1-i)].Express z1z3/z2,z1z2/z3,and z1/z3z2 in both polar and standard forms.

the roots of the equation z^4+az^3+(12+9i)az^2+bz=0( where a nd b are complex numbers) are the vertices of a square

If z is a complex number and |z + 16| = 4 |z + l|, find the value of | z|

if f(z) is an analytical function of z, then prove that ( d^2/dx^2 + d^2/ dy^2) log |f(z)|= 0

Expand f(z)=𝑧+3/𝑧(𝑧2−𝑧−2) in power of z where

a) |𝑧|<1

b) 1<|𝑧|<2

c) |𝑧|>2