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Elementary algebra of complex variables problem

  • Thread starter jdinatale
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  • #1
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I'm having difficulty deducing that Re z = 0.

w00r3b.jpg
 

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  • #2
vela
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Try multiplying the top and bottom by (1-w*).
 
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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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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
Dick
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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.
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
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The calculation shows z is pure imaginary
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...
 
  • #8
Dick
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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...
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
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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?
Ha-ha! I was right!!!

A complete face-palm...

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

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