The value of $(1+i)^5(1-i)^7$ 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

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

Let $z$ be a complex number with $\operatorname{Im}(z)=10$ and satisfying $\frac{2z-n}{2z+n}=2i-1$, where $i=\sqrt{-1}$, for some natural number $n$. Then:

If $x = -2 - \sqrt{3} i$,where $i = \sqrt{-1}$,then the value of $2x^4 + 5x^3 + 7x^2 - x + 41$ is

If $\frac{1-10 i \cos \theta}{1-10 \sqrt{3} i \sin \theta}$ is purely real,then one of the values of $\theta$ is