Suppose, $$\omega$$ is a cube root of unity with $$\omega$$ $$\ne$$ 1. Suppose, P and Q are the points on the complex plane defined by $$\omega$$ and $$\omega$$². If O is the origin, then what is the angle between OP and OQ?

Suppose, $$\omega$$₁ and $$\omega$$₂ are two distinct cube roots of unity different from 1. Then, what is $${({\omega _1} - {\omega _2})^2}$$ equal to?

The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$, is

If $$\left| {z - {4 \over z}} \right| = 2$$, then the maximum value of $$\left| z \right|$$ is equal to