Elementary algebra of complex variables problem

1. Aug 28, 2012

jdinatale

I'm having difficulty deducing that Re z = 0.

2. Aug 28, 2012

vela

Staff Emeritus
Try multiplying the top and bottom by (1-w*).

3. Aug 28, 2012

jdinatale

Thank you, that seems to work. Can you confirm that this is correct?

http://i45.tinypic.com/2wc2xl4.png

Last edited by a moderator: Aug 28, 2012
4. Aug 28, 2012

vela

Staff Emeritus
You made a minor error in calculating the denominator when you canceled the ones.

5. Aug 28, 2012

skiller

Sorry for butting in, but although I can see where jdinatale went wrong in his last post, I still can't see how Re(z) can be proved to be zero.

Of course it's correct, but I can't quite see it.

6. Aug 29, 2012

Dick

The calculation shows z is pure imaginary and that's still true after you make the correction. Doesn't that show Re(z)=0?

7. Aug 29, 2012

skiller

How does it?

Sorry, I'm probably being very thick here and will live to regret it.

How does

$$z = (1 + \omega) / (1 - \omega)$$
where $\omega = e^{ik\pi/50}$

imply that $z$ is purely imaginary?

Like I say, I know it's correct to say so, but I'm lost on how to prove it - even after trying using the conjugate method as offered above.

It'll probably be a face-palm moment when I find out...

8. Aug 29, 2012

Dick

Look at what happens when jdinatale multiplies by (1+w*). The results has w-w* (which is pure imaginary) in the numerator and w+w* (which is pure real) in the denominator. What kind of a number is imaginary/real?

9. Aug 29, 2012

skiller

Ha-ha! I was right!!!

A complete face-palm...

Thanks for that. I blame my incompetence on my getting on a bit.