The equation whose solutions are the non-zero solutions of the equation $\bar{z}=i z^2$ is:

If $Z_1$ and $Z_2$ are two non-zero complex numbers,then which of the following is not true?

$\omega$ is a complex cube root of unity and if $Z$ is a complex number satisfying $|Z-1| \leq 2$ and $|\omega^2 Z-1-\omega|=a$,then the set of possible values of $a$ is

If $\cos A+\cos B+\cos C=0$ and $\sin A+\sin B+\sin C=0$,then $\cos (A-B)=$

If $i = \sqrt{-1}$, then $\frac{e^{xi} + e^{-xi}}{2} = $

If $\sqrt{5}-i \sqrt{15}=r(\cos \theta+i \sin \theta)$ where $-\pi < \theta < \pi$,then find the value of $r^2(\sec \theta+3 \operatorname{cosec}^2 \theta)$.