### Complex Numbers

goals
A is a region such that $\cfrac{z}{4}$ and $\cfrac{4}{\bar{z}}$  have their real and imaginary parts $\epsilon$ (0, 1). If P $=$ area of region A then [P] equals?  ([x] represents greatest integer x)

In the multiplicative group of $n$th roots of unity, the inverse of ${ \omega }^{ k }$ is $(k< n)$:
A is a region such that $\cfrac{z}{4}$ and $\cfrac{4}{\bar{z}}$  have their real and imaginary parts $\epsilon$ (0, 1). If P $=$ area of region A then [P] equals?  ([x] represents greatest integer x)

If $\displaystyle z_{0}=\frac{1-i}{2}$,  then $\displaystyle \left (1+z_{0} \right )\left (1+z_{0}^{{2}^{1}} \right )\left (1+z_{0}^{{2}^{2}} \right ).......... \left (1+z_{0}^{2^n} \right )$  must be
If $z_1 = 5 + 12i$  &   $|z_2| = 4$ then