Complex numbers are numbers that can be expressed in the form of a+bi. Complex numbers are a combination of real and imaginary numbers where a and b are real numbers and i is an imaginary unit. Complex numbers exist because they are needed in order to solve problems seen in geometry, calculus, physics and more.
The Fundamental Theorem of Algebra says all non-constant single-variable polynomials with complex coefficents have at least one complex root. The theorem needs complex numbers in order to make polynomials equal to zero in some cases.