If $|Z|=2, Z_1=\frac{Z}{2} e^{i \alpha}$ and $\theta$ is the $\operatorname{amp}(Z)$, then $\frac{Z_1^n-Z_1^{-n}}{Z_1^n+Z_1^{-n}}=$

If $n, K \in N$ such that $n \neq 3 K$, then $(\sqrt{3}+i)^{2 n}+(\sqrt{3}-i)^{2 n}=$

In argand plane, no value of $\sqrt[3]{1-i \sqrt{3}}$ lie in

If $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$, then $3 x+y=$