Find the number of non-zero integral solutions of the equation $|1-i|^{x}=2^{x}$

Let $z_1$ and $z_2$ be two complex number such that $z_1$ $+z_2=5$ and $z_1^3+z_2^3=20+15 i$. Then $\left|z_1^4+z_2^4\right|$ equals-

Let $z =1+ i$ and $z _1=\frac{1+ i \overline{ z }}{\overline{ z }(1- z )+\frac{1}{ z }}$. Then $\frac{12}{\pi}$ $\arg \left(z_1\right)$ is equal to $……….$.

If ${Z_1} \ne 0$ and $Z_2$ be two complex numbers such that $\frac{{{Z_2}}}{{{Z_1}}}$ is a purely imaginary number, then $\left| {\frac{{2{Z_1} + 3{Z_2}}}{{2{Z_1} – 3{Z_2}}}} \right|$ is equal to 

Let $z$ =${i^{2i}}$ , then $|z|$ is (where $i$ =$\sqrt { – 1}$ )