9 - Complex Numbers in The Fundamental Theorem of Algebra

A postulate of the fundamental theorem of algebra is that a polynomial of degree n has n roots.

When we have a n-th degree polynomial, if it doesn't have real roots, it will have complex roots.

You can't just have one complex root for a polynomial. Complex roots always come in pairs. So, a conjugate pair.
Suppose you find a complex number z is a root of our polynomial of degree n. Then, necessarily, its complex conjugate MUST also be a root.