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 –

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) – $arg $({z_2})$ is equal to

Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w – \overline {w}z  = k\left( {1 – z} \right)$ , for some real number $k$, is

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