Imaginary Zero :

Let us consider a factor of an imaginary zero as .

A factor with an imaginary zero is .

Since is a factor of the imiganary zero, must also be a factor.

Irrational zero :

Irrational zeros are not rational.

Let us consider an irrational zero .

Since the function has a degree of ,let ia also a root.

The function can be written as .

The fourth degree function with an imiginary zero and irrational zero is .