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

Geometrically $${\mathop{\rm Re}\nolimits} ({z^2} - i) = 2$$, where, $$i = \sqrt { - 1} $$ and Re is the real part, represents