If ${z_1}.{z_2}........{z_n} = z,$ then $arg\,{z_1} + arg\,{z_2} + ....$+$arg\,{z_n}$ and $arg$$z$ differ by a

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

Find the modulus and argument of the complex numbers:

$\frac{1}{1+i}$

Find the modulus and the argument of the complex number $z=-\sqrt{3}+i$

If $a > 0$ and $z = \frac{{{{\left( {1 + i} \right)}^2}}}{{a - i}}$, has magnitude $\sqrt {\frac{2}{5}} $, then $\bar z$ is equal to:

Let $a \neq b$ be two non-zero real numbers.Then the number of elements in the set $X =\left\{ z \in C : \operatorname{Re}\left(a z^2+ bz \right)= a \text { and }\operatorname{Re}\left(b z^2+ az \right)= b \right\}$ is equal to