Math basics › Precalculus
Complex numbers
i is the square root of minus one
i² = −1. The powers cycle every four: i, −1, −i, 1, and round again.
Arithmetic
Add and subtract the real and imaginary parts separately. Multiply like binomials, then replace i² with −1.
Dividing
Multiply top and bottom by the conjugate of the bottom. (a + bi) and (a − bi) multiply to a² + b², which is real.
Where they come from
A negative discriminant. The parabola misses the x-axis, so the roots are a conjugate pair.