Question

Complex roots. Please help!

Answer 1

Using DeMoivre's theorem, and the fact that any root in the first quadrant has argument between $0^\circ$ and $90^\circ$, we get

$16i=16\left(\cos90^\circ+i\sin90^\circ)\implies\sqrt{16i}=\sqrt{16}\left(\cos45^\circ+i\sin45^\circ\right)$

so the missing value is 45.