Complex Numbers

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