Easy way to solve $w^2 = -15 + 8i$ 
Solve $w^2=−15+8i$, where $w$ is complex.

Normally, I would convert this into polar coordinates, but the problem is that is too slow. 
What is another alternative? 

Start out by letting $w = a + bi \implies w^2 = a^2-b^2 + 2abi = -15+8i \implies a^2-b^2 = -15, 2ab = 8 \implies a^2 - \dfrac{16}{a^2} = -15$. Put $x = a^2 \implies x - \dfrac{16}{x} + 15 = 0\implies x^2 + 15x - 16 = 0\implies (x-1)(x+16) = 0\implies x = 1\implies a = \pm 1, b = \pm 4$
