If $|{z_1} + {z_2}| = |{z_1} – {z_2}|$, then the difference in the amplitudes of ${z_1}$ and ${z_2}$ is

If $z$ is a complex number such that  $\left| z \right| \ge 2$ , then the minimum value of $\left| {z + \frac{1}{2}} \right|$: 

The solutions of equation in $z$, $| z |^2 -(z + \bar{z}) + i(z – \bar{z})$ + $2$ = $0$ are $(i = \sqrt{-1})$

If ${z_1} = a + ib$ and ${z_2} = c + id$ are complex numbers such that $|{z_1}| = |{z_2}| = 1$ and $R({z_1}\overline {{z_2}} ) = 0,$ then the pair of complex numbers ${w_1} = a + ic$ and ${w_2} = b + id$ satisfies

If $\sqrt 3 + i = (a + ib)(c + id)$, then ${\tan ^{ – 1}}\left( {\frac{b}{a}} \right) + $ ${\tan ^{ – 1}}\left( {\frac{d}{c}} \right)$ has the value