If a complex number $z$ satisfies the equation $z + \sqrt{2} |z + 1| + i = 0$,then $|z|$ 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

If $z=x+iy$ is a complex number such that $\bar{z}^{\frac{1}{3}}=a+ib$,then the value of $\frac{1}{a^2+b^2}\left(\frac{x}{a}+\frac{y}{b}\right)$ is equal to

If $(x-iy)^{1/3} = 2-i\sqrt{3}$ and the point $z = (x, y)$ lies on the line $\frac{x}{2} + \frac{y}{\sqrt{3}} = k$,then $k =$

If $z_{1}, z_{2}, z_{3}$ are complex numbers such that $|z_{1}|=|z_{2}|=|z_{3}|=|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}|=1$, then $|z_{1}+z_{2}+z_{3}|$ is

Sum of the squares of the imaginary roots of the equation $z^8-20z^4+64=0$ is