- #1

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I'm having difficulty deducing that

**Re**z = 0.-
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- Thread starter jdinatale
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- #1

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

- #2

vela

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Try multiplying the top and bottom by (1-w^{*}).

- #3

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Thank you, that seems to work. Can you confirm that this is correct?Try multiplying the top and bottom by (1-w^{*}).

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

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- #4

vela

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

- #5

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

- #6

Dick

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

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

- #7

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How does it?The calculation shows z is pure imaginary

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

How does

[tex]z = (1 + \omega) / (1 - \omega)[/tex]

where [itex]\omega = e^{ik\pi/50}[/itex]

imply that [itex]z[/itex] 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

Dick

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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?How does it?

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

How does

[tex]z = (1 + \omega) / (1 - \omega)[/tex]

where [itex]\omega = e^{ik\pi/50}[/itex]

imply that [itex]z[/itex] 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...

- #9

- 237

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Ha-ha! I was right!!!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?

A complete face-palm...

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

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