How can I prove that and is a root of the polynomial

Using

I have been able to prove but I dont get how to use that to show that and are roots of the polynomial.

Thanks in advance for your help!

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- November 1st 2012, 10:40 AMflametag3how to prove z0 is a root of the polynomial
How can I prove that and is a root of the polynomial

Using

I have been able to prove but I dont get how to use that to show that and are roots of the polynomial.

Thanks in advance for your help! - November 1st 2012, 07:16 PMchiroRe: how to prove z0 is a root of the polynomial
Hey flametag3.

Is this asking to show that if z0 is a root then z0_bar is a root or is it asking that if the condition (z_bar)^k = (z^k)_bar, then that particular z is a root for when that is true? - November 2nd 2012, 10:08 PMflametag3Re: how to prove z0 is a root of the polynomial
Hey Chiro,

thanks for your reply. Its asking to show that if z0 is a root then z0_bar is a root as well. - November 2nd 2012, 11:35 PMchiroRe: how to prove z0 is a root of the polynomial
You'll have to show that if z gives 0 then z_bar also gives 0, and one to show that given what you have is to show that the equation with z_bar is zero if the one with z is zero and you will need to apply this term by term in your polynomial to show that both equal zero and thus both are roots of the polynomial if they have a specific f(z) form (note f(z) doesn't change but z = z or z = z_bar both need to give f(z) = 0 to both be roots).