Find square root of `8-15 i`

Explanation

Let `a+ib=sqrt(8-15i)`

`(a=ib)^2=8-15i`

`a^2-b^2=2abi=8-15i`

`a^2-b^2=8------(1)` and `2ab=-15`

`(a^2+b^2)^2=289=>a^2+b^2=17------(2)`

From equation (1) and (2), we get, `a=+-frac{5}{sqrt(2)}` and `b=+-frac{3}{sqrt(2)}`

`:.+-(frac{5}{sqrt(2)} + i frac{3}{sqrt(2)})`