If $z =2+3 i$, then $z ^{5}+(\overline{ z })^{5}$ is equal to.

If complex numbers $z_1$, $z_2$ are such that $\left| {{z_1}} \right| = \sqrt 2 ,\left| {{z_2}} \right| = \sqrt 3$ and $\left| {{z_1} + {z_2}} \right| = \sqrt {5 - 2\sqrt 3 }$, then the value of $|Arg z_1 -Arg z_2|$ is

If $z$ is a complex number such that $|z - \bar{z}| = 2$ and $|z + \bar{z}| = 4 $, then which of the following is always incorrect -

If $|{z_1}|\, = \,|{z_2}|$ and $amp\,{z_1} + amp\,\,{z_2} = 0$, then

The maximum value of $|z|$ where z satisfies the condition $\left| {z + \frac{2}{z}} \right| = 2$ is

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