Complex numbers are written as (a + bi), where (a) and (b) are regular numbers. These numbers can make solving some polynomial equations tricky.

A lot of polynomials, especially those without real roots, need complex solutions. This means we have to really understand how imaginary units work.

Here are some of the main challenges:

• Finding roots: It can be tough to tell when there are complex roots.
• Doing the math: Working with complex numbers can make calculations more complicated.

But don’t worry! The Fundamental Theorem of Algebra tells us that every polynomial of degree (n) has exactly (n) roots. These roots can be real or complex. This theorem helps us find solutions, even if it’s not always easy.