If $i=\sqrt{-1}$, then $\sum\limits_{n=2}^{30} i^n+\sum\limits_{n=30}^{65} i^{n+3}=$

If $z_1$ and $z_2$ are two of the $n$th roots of unity such that the line segment joining them subtends at a right angle at the origin, then for a positive integer $k, n$ takes the form

$$ (\sqrt{\sqrt{2}+1}+i \sqrt{\sqrt{2}-1})^8= $$

If the harmonic mean of the roots of the equation $\sqrt{2} x^2-b x+(8-2 \sqrt{5})=0$ is