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Math Help - [SOLVED] Complex Number Problem

  1. #1
    Junior Member Evales's Avatar
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    [SOLVED] Complex Number Problem

    Question:
    Solve for z, in exact polar form, in the equation z(z - c) = -c^2 where c is a some positive constant.
    Plot the solutions on the Argand plane.

    My workings
    z(z - c) = -c^2
    z^2 - zc = -c^2
    z^2 = zc - c^2

    My queries:
    How do I isolate the z/ do I need to?
    This question asks for ploting points does that mean I need actual values?
    If yes how do I get actual values out of the question?
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Evales View Post
    Question:
    Solve for z, in exact polar form, in the equation z(z - c) = -c^2 where c is a some positive constant.
    Plot the solutions on the Argand plane.

    My workings
    z(z - c) = -c^2
    z^2 - zc = -c^2

    Mr F says: {\color{red}\Rightarrow z^2 - c z + c^2 = 0}

    Use the quadratic formula and simplify the result:

    {\color{red} \Rightarrow z = \frac{c(1 \pm i \sqrt{3})}{2}}

    [snip]
    ..
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  3. #3
    Junior Member Evales's Avatar
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    Thanks a lot! I can't believe I didn't think of that
    Last edited by Evales; August 7th 2008 at 01:03 AM.
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