We have x^4 - 1 = 0 => ( x^2 + 1 )(x^2 - 1 ) = 0
gives x^2 = 1 and x^2 = -1
so roots of equation are 1; -1; i; -i
At the time I had posted it, I had completely forgotten about this formula. At some point, I remembered using it for complex numbers, and needed to double check that it was useable for just real numbers.
I also didn't know if I was overcomplicating things, and if there was an easier way to do it.