If $z = x + iy$ is a complex number such that $z\bar{z}^3 + \bar{z}z^3 = 350$ and $x, y$ are integers,then $|z| = $

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

Let $a, b$ be two real numbers such that $ab < 0$. If the complex number $\frac{1+ai}{b+i}$ is of unit modulus and $a+ib$ lies on the circle $|z-1|=|2z|$,then a possible value of $\frac{1+[a]}{4b}$,where $[t]$ is the greatest integer function,is:

If $z=\cos 6^{\circ}+i \sin 6^{\circ}$,then $\sum_{n=1}^{20} \operatorname{Im}\left(z^{2 n-1}\right)=$

Consider the regions for complex number $z$ defined by $A: \frac{1}{\log_2 |z|} - \frac{1}{\log_2 |z| - 1} - 1 < 0$ and $B: \operatorname{Im}(z) = 0$. The range of values of $\operatorname{Re}(z)$ lying in the region $A \cap B$ is

The set of all values of $\theta$ such that $\frac{1-i \cos \theta}{1+2 i \sin \theta}$ is purely imaginary is