complex are numbers that can be expressed in the for a+bi, where a and b are real numbers and i is the imaginary unit, using the equation i^2 = -1. in this expression a is the real part and b is the imaginary part of the complex number.
The fundamental theorem of algebra or FTA states that if there is a second degree polynomial, then there must be exactly 2 roots. The FTA needs complex numbers in order to be true because the complex are what makes the equation true.