This is a complex quadratic, so you can proceed by completing the square,Originally Posted by phgao
or using the quadratic formula to find its roots and then the
So lets simplify the equation a bit:
The only problem will be finding the square root of the discriminant.
In this case the discriminant is:
We need the square root of this. We proceed by converting the discriminant
to polar form, then finding the square root by square-rooting the modulus and
halving the argument. Or as MathWorld would put it:
Which should allow you to complete the factorisation.