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

If $1+2i$ is a root of the equation $x^4-3x^3+8x^2-7x+5=0$,then the sum of the squares of the other roots is

$\begin{aligned} & \text{If } z=e^{i \theta} \text{ and } \frac{3 \cos 3 \theta+2 \cos 2 \theta+5 \cos 5 \theta}{3 \sin 3 \theta+2 \sin 2 \theta+5 \sin 5 \theta} \\ & =\frac{i \sum_{r=0}^{10} a_r z^r}{\sum_{r=0}^{10} b_r z^r} \text{ then } \frac{\left(\sum_{r=0}^{10} a_r+\sum_{r=0}^{10} b_r\right)}{10}= \end{aligned}$

The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3$ is

Let $z$ and $w$ be two distinct non-zero complex numbers. If $|z|^2 w - |w|^2 z = z - w$,then:

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