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Math Help - Mapping

  1. #1
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    Mar 2011
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    Mapping

    Hi

    I need a help in solving the following problem. the problem says: find the image of the unit circle |z|=1, under the mapping w=2z+z^2.

    Thanks
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  2. #2
    Member mohammadfawaz's Avatar
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    Lebanon - Beirut
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    Given a point on the unit circle, it will have the form z=e^{(it)} where 0\leq t \leq 2\pi. Have: w=2z+z^2 = 2e^{(it)}+e^{(2it)}.
    This means that the real part is x=2cos(t)+cos(2t) and the imaginary part is y=2sin(t)+sin(2t). These are the parametric equations of a cardioid. You can take several values of t and try to draw it.
    Cardioid - Wikipedia, the free encyclopedia
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  3. #3
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    Thanks Mr. Fawwaz I have reached x and y but I did not know how to proceed.
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