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Math Help - Graph of a complex function?

  1. #1
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    Cool Graph of a complex function?

    The 2D graph of the complex function z=cos(theta)-isin(theta) is a circle centered at the origin. The direction of the graph is CLOCKWISE.

    WHY ?
    Last edited by Jhevon; April 25th 2009 at 07:47 PM.
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  2. #2
    MHF Contributor
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    Argand diagram

    Hello Mohit
    Quote Originally Posted by Mohit View Post
    The 2D graph of the complex function z=cos(theta)-isin(theta) is a circle centered at the origin. The direction of the graph is CLOCKWISE.

    WHY ?
    The reason is quite straightforward.

    z = \cos\theta \color{red}+\color{black} i\sin\theta represent a circle, centre O, in an anticlockwise direction. If we want a circle to go clockwise, we must replace \theta by -\theta. Then we get the equation:

    z = \cos(-\theta) + i\sin(-\theta)

    Agreed?

    But \cos(-\theta) = \cos\theta and \sin(-\theta) =-\sin \theta, so this becomes

    z = \cos\theta - i\sin\theta

    OK?

    Grandad
    Last edited by mr fantastic; April 25th 2009 at 09:11 PM.
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  3. #3
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    thx, i understand
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