# Complex roots in conjugate pairs

• Sep 23rd 2010, 11:11 PM
arze
Complex roots in conjugate pairs
Given that $p+iq$, where p and q are real and $q\neq 0$, is a root of the equation
$a_0 z^n+a_1 z^{n-1}+...+a_n$
where $a_0, a_1, ..., a_n$ are all real, prove that $p-iq$ 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
• Sep 23rd 2010, 11:23 PM
mr fantastic
Quote:

Originally Posted by arze
Given that $p+iq$, where p and q are real and $q\neq 0$, is a root of the equation
$a_0 z^n+a_1 z^{n-1}+...+a_n$
where $a_0, a_1, ..., a_n$ are all real, prove that $p-iq$ 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

http://en.wikipedia.org/wiki/Complex...e_root_theorem