Given that $z$ is a real number and $z=\frac{\lambda+4 i}{1+\lambda i}$ where $\lambda \in R$, then the possible value of $\lambda$ is :

If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then

The complex number $\frac{1+7 i}{(2-i)^2}$ lies in

If $\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$ then $(y, x)=$