Simple Proof
One proof of the theorem is as follows:
Consider the polynomial
where all ar are real. Suppose some complex number ζ is a root of P, that is P(ζ) = 0. It needs to be shown that
as well.
If P(ζ) = 0, then
which can be put as
Now
and given the properties of complex conjugation,
Since,
it follows that
That is,
Read more about this topic: Complex Conjugate Root Theorem
Famous quotes containing the words simple and/or proof:
“The good old rule
Sufficeth them, the simple plan,
That they should take, who have the power,
And they should keep who can.”
—William Wordsworth (1770–1850)
“O, popular applause! what heart of man
Is proof against thy sweet, seducing charms?”
—William Cowper (1731–1800)