If $z = x + iy$,${z^{1/3}} = a - ib$ and $\frac{x}{a} - \frac{y}{b} = k({a^2} - {b^2})$,then the value of $k$ is equal to:

If $2i$ is a root of $f(z) = z^4 + z^3 + 2z^2 + 4z - 8 = 0$,then which among the following cannot be a root of $f(z) = 0$?

If $z = 3 - 4i$,then ${z^4} - 3{z^3} + 3{z^2} + 99z - 95$ is equal to

If $a = \frac{1 - i \sqrt{3}}{2}$, then the correct matching of List-$I$ with List-$II$ is:

List-$I$	List-$II$
$(i)$ $a \bar{a}$	$(A)$ $-\frac{\pi}{3}$
$(ii)$ $\arg \left(\frac{1}{\bar{a}}\right)$	$(B)$ $-i \sqrt{3}$
$(iii)$ $a - \bar{a}$	$(C)$ $2i / \sqrt{3}$
$(iv)$ $\operatorname{Im}\left(\frac{4}{3a}\right)$	$(D)$ $1$
	$(E)$ $\pi / 3$
	$(F)$ $\frac{2}{\sqrt{3}}$

If $x$ and $y$ are two positive real numbers such that $x+iy = \frac{13 \sqrt{-5+12i}}{(2-3i)(3+2i)}$,then $13y-26x=$

If $\alpha, \beta$ and $\gamma$ are angles that satisfy the following conditions, find the value of $xyz$.
$1.$ $\tan \alpha + \tan \beta + \tan \gamma = \tan \alpha \tan \beta \tan \gamma$
$2.$ $x = \cos \alpha + i \sin \alpha$
$3.$ $y = \cos \beta + i \sin \beta$
$4.$ $z = \cos \gamma + i \sin \gamma$