If $x = -5 + 2 \sqrt{-4}$,then the value of $x^4 + 9x^3 + 35x^2 - x + 4$ is

Let $z$ be a complex number such that $|z|=1$. If $\frac{2+k^2z}{k+\overline{z}}=kz$,where $k \in R$,then the maximum distance of $k+ik^2$ from the circle $|z-(1+2i)|=1$ is:

If $x=p+q$,$y=p \omega+q \omega^2$ and $z=p \omega^2+q \omega$,where $\omega$ is a complex cube root of unity,then $xyz$ is equal to

Let $S = \{z \in \mathbb{C} : z^2 + 4z + 16 = 0\}$. Then $\sum_{z \in S} |z + \sqrt{3}i|^2$ is equal to:

The number of solutions for $z^3+\bar{z}=0$ is

If $a, b \in \mathbb{R}$ and $i=\sqrt{-1}$,then the number of ordered pairs of real numbers $(a, b)$ satisfying the condition $(a+bi)^3 = a-bi$ is