just a quadratic ....
x^2 + 1 - i = 0
x = (-1 ± √(1 - 4(1)(-i))/2
= (-1 ± √(4i + 1) ) / 2
Don't know at what level you have studied complex numbers.
DeMoivre's Theorem ring a bell?
x2 + 1 - i = 0
2 answers
so, moving on and using DeMoivre's Theorem, and converting back to rectangular form, you end up with
x = ±∜2 (√(2+√2)/2 - √(2-√2)/2 i)
x = ±∜2 (√(2+√2)/2 - √(2-√2)/2 i)