# Addition of complex conjugates by induction

• Dec 13th 2011, 06:00 AM
Johngalt13
Addition of complex conjugates by induction
prove that overbar/(z1 + z2 + .... + zn) = overbar(z1) + overbar(z2) + .... +overbar(zn)

I showed true for n = 2 already
I then assumed true for n = k and wrote out the induction hypothesis
Then of course I need to show true for n = k + 1 and substitute the induction hypothesis in. So I came out with

overbar(z1 + z2 + .... + zn + zn+1) = overbar/(z1 + z2 + .... + zn) + overbar(zn+1)

I know I'm close, and I'm sure it's something simple that I'm missing but I don't know what to do next.

Any help?
• Dec 13th 2011, 06:12 AM
Plato
Re: Addition of complex conjugates by induction
Quote:

Originally Posted by Johngalt13
prove that overbar/(z1 + z2 + .... + zn) = overbar(z1) + overbar(z2) + .... +overbar(zn)
I showed true for n = 2 already
I then assumed true for n = k and wrote out the induction hypothesis
Then of course I need to show true for n = k + 1 and substitute the induction hypothesis in. So I came out with

$\overline{(z_1 + z_2 + .... + z_n + z_{n+1})} = \overline{(z_1 + z_2 + .... + z_n)} + \overline{z_{n+1}}$

You are right there.
You know it works for two numbers as well as $\overline{(z_1 + z_2 + .... + z_n)}$
• Dec 13th 2011, 06:26 AM
Johngalt13
Re: Addition of complex conjugates by induction
Quote:

Originally Posted by Plato
You are right there.
You know it works for two numbers as well as $\overline{(z_1 + z_2 + .... + z_n)}$

Edit:Nevermind I got it, thanks that helped!