Complex numbers (conjugate,modulus,etc)

If z is a complex number of unit modulus and argument theta , then the real part of (z(1-barz))/(barz(1+z)) , is

Find the sum and product of the complex number (3-4i) with its conjugate.

Let n be a positive integer and a complex number with unit modulus is a solution of the equation Z^n+Z+1=0 , then the value of n can be

Find the sum and product of the complex number (-1 +2i) with its conjugate.

Find the conjugate, modulus and argument of sqrt(2)-sqrt(2)i

Find the modulus and argument of the following complex number and convert them in polar form: (1+3i)/(1-2i)

Suppose p is a polynomial with complex coefficients and an even degreen. If all the roots of p are complex non-real numbers with modulus 1, prove that p(1) in R iff p(-1) in R

Find the modulus and argument of the following complex number and convert them in polar form: (i-1)/[cos(pi/3)+isin(pi/3)]

Represent the following complex numbers in the complex plane i

Let z be a complex number (not lying on x-axis) of maximum modulus such that |z+1/z|=1 . Then,