Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is

If $z_1, z_2, z_3$ $\in$  $C$ such that $|z_1| = |z_2| = |z_3| = 2$, then greatest value of expression $|z_1 - z_2|.|z_2 - z_3| + |z_3 - z_1|.|z_1 - z_2| + |z_2 - z_3||z_3 - z_1|$ is

If ${z_1},{z_2}$ are two complex numbers such that $\left| {\frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}} \right| = 1$ and $i{z_1} = k{z_2}$, where $k \in R$, then the angle between ${z_1} - {z_2}$ and ${z_1} + {z_2}$ is

The amplitude of $\frac{{1 + \sqrt 3 i}}{{\sqrt 3 + 1}}$ is

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

Let $z_1 = 6 + i$ and $z_2 = 4 -3i$. Let $z$ be a complex number such that $arg\ \left( {\frac{{z - {z_1}}}{{{z_2} - z}}} \right) = \frac{\pi }{2}$, then $z$ satisfies -