For $k>0$,if $k \sqrt{-1}$ is a root of the equation $x^4+6 x^3-16 x^2+24 x-80=0$,then $k^2=$

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

If $\sqrt{-3-4 i}=re^{i \theta}$,then $r^2 \tan \theta=$

Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of $(\bar{z})^2+\frac{1}{z^2}$ are integers,then which of the following is/are possible value$(s)$ of $|z|$?

If $z_1$ and $z_2$ are any two complex numbers,then $|z_1 + \sqrt{z_1^2 - z_2^2}| + |z_1 - \sqrt{z_1^2 - z_2^2}|$ is equal to

$\omega$ 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