The Fundamental Theorem of Algebra

Any polynomial of degree "n" has "n" roots

however, the roots can be complex (imaginary)

This function has 4 roots, since the highest exponent is 4


A function can also be rewritten using its roots:

This function has 2 roots because of the 2nd degree exponent

Factor into :
The roots are 4 and -4, so the equation can be rewritten using the roots to read:

Imaginary roots:
If a function's highest degree is 5, there will always be 5 roots. However, some of these roots may be imaginary, or, complex.

If a root is complex, its conjugate must also be complex.

Therefore, complex roots come in pairs and there will always be an even amount of them.

For example, the following equation has 2 roots. They are both imaginary though, because: