1. The difference of Z and its conjugate is an imaginary number.

2. The sum of Z and its conjugate is a real number.

What is the modulus of the complex number i^{2n + 1}(-i)^{2n - 1}, where n ∈ N and i = √-1?

The smallest positive integer n for which

$\rm \left(\frac{1-i}{1+i}\right)^{n^2}=1$

where i = √-1, is

If Z = 1 + i, where i = √-1, then what is the modulus of $\rm z+\frac{2}{z}?$