Let $$\mathrm{p,q\in\mathbb{R}}$$ and $${\left( {1 - \sqrt 3 i} \right)^{200}} = {2^{199}}(p + iq),i = \sqrt { - 1} $$ then $$\mathrm{p+q+q^2}$$ and $$\mathrm{p-q+q^2}$$ are roots of the equation.

If $$z \neq 0$$ be a complex number such that $$\left|z-\frac{1}{z}\right|=2$$, then the maximum value of $$|z|$$ is :

Let $$\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=|z-1|\}$$. Then the set of all values of $$x$$, for which $$w=2 x+i y \in \mathrm{S}$$ for some $$y \in \mathbb{R}$$, is :

If $$z=2+3 i$$, then $$z^{5}+(\bar{z})^{5}$$ is equal to :