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Math Help - complex functions

  1. #1
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    complex functions

    Hi,

    Q1.
    a) Find all complex-valued solutions to the equation z^3 - 2z^2 + 4z by hand. Write each one in the form a+bi.

    b) Starting with the real-valued root, sketch all the complex-valued cuve roots of -27 in the complex plane. Against each, write its value in the form re^i(feta)


    If there is anything unclear in the question, let me know, thanks.
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  2. #2
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    Quote Originally Posted by Moon Hoplite View Post
    Hi,

    Q1.
    a) Find all complex-valued solutions to the equation z^3 - 2z^2 + 4z by hand. Write each one in the form a+bi.

    Mr F says: z(z^2 - 2z + 4). Factorise the quadratic by first completing the square.

    b) Starting with the real-valued root, sketch all the complex-valued cuve roots of -27 in the complex plane. Against each, write its value in the form re^i(feta)
    Mr F says: The real root cube root of -27 is -3. All the cube roots lie on a circle of radius 3 and are equally spaced by angle 2 pi/3 ....


    If there is anything unclear in the question, let me know, thanks.
    ..
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  3. #3
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    in Q1, how does it mean by giving the answer in the form a+bi?

    and in Q2., i still dont get it - is there any key words where i could research the topic based on this question?
    Last edited by Moon Hoplite; January 31st 2009 at 07:09 PM. Reason: added question
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  4. #4
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    Quote Originally Posted by Moon Hoplite View Post
    in Q1, how does it mean by giving the answer in the form a+bi?
    Factor the quadratic and the answer should be clear.
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