What is $ \left( \frac{\sqrt{3}+i}{\sqrt{3}-i} \right)^3 $ equal to?

If $z\ne0$ is a complex number, then what is $amp(z)+amp(\bar{z})$ equal to?

If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?  

What is the value of the sum $\rm \sum\limits_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})$ where i = √-1 ?