Given that $\displaystyle p+iq$, where p and q are real and $\displaystyle q\neq 0$, is a root of the equation

$\displaystyle a_0 z^n+a_1 z^{n-1}+...+a_n$

where $\displaystyle a_0, a_1, ..., a_n$ are all real, prove that $\displaystyle p-iq$ is also a root.

This is the first part of the question, its the harder part. Second part is about finding constants from roots, two of which are complex.

How do I start? I know its true, but how do I prove it?

Thanks