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√(16i)=√(16)\left(\cos45^\circ+i\sin45^\circ\right)`

so the missing value is 45.