Complex Analysis Answers

4. What is the value of

sum - infty ^ infty 1/{ (z+n)^ 2 +a^2}?

y"-4y'+9y=t,y(0)=0,y'(0)=1, find the transfer function

Given two complex numbers z and w such that z=(1+i)w+(3-i)w^_ where w^_is the conjugate of w which of the following is w^_ in terms of z and z^_

A complex number z satisfies the equation z^2=3 +4i which of the following is true about z?

If Z=a+bi/c+di where a, b, c and d are real quantities, show that (a) if z is real then a/b=c/d and (b) if z is entirely imaginary then a/b=-d/c

If x and y are real, solve the equation
jx/1+jy=3x+4j/x+3y

It is given that 

z+2i=iz+λ, (w/z)=2+2i, Imw=8

where z and w are complex numbers, and λ is a real constant. Which of the following is the value of λ? 

1. λ=4
2. λ=8
3. λ=3
4. λ=-3
5. λ=-4

Express z 1⁄4 e1þj=2 in the form a þ j

A complex number z satisfies the equation 

z^2\:=3+4i.

Which of the following is true about z?

1. (3+4i)^2=25+24i
2. z=+-(2+i)
3. (3+4i)^2=9+40i
4. z=+-(2+2i)
5. (3+4i)^2=7+24i