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Math Help - Finding Complex Solutions

  1. #1
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    Finding Complex Solutions

    Hey,
    I'm not sure if i'm posting my question in the right forum, as it has to with complex numbers, but i will ask anyway and hopefully someone can help! I need to find all of the complex solutions for:
    z^5 = i
    Is anyone able to help me start this question?
    Do i need to find i in polar form?

    Thanks,
    Function
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  2. #2
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    Quote Originally Posted by function View Post
    Hey,
    I'm not sure if i'm posting my question in the right forum, as it has to with complex numbers, but i will ask anyway and hopefully someone can help! I need to find all of the complex solutions for:
    z^5 = i
    Is anyone able to help me start this question?
    Do i need to find i in polar form?

    Thanks,
    Function
    Note that z^5 = r^5 \text{cis} (5 \theta) and i = \text{cis} \left( \frac{\pi}{2} + 2n \pi\right) where n is an integer.


    Edit: To save me some Moderating work, the following thread is probably relevant to what you're going to ask next: http://www.mathhelpforum.com/math-he...lex-roots.html. So don't ask it here ....
    Last edited by mr fantastic; August 18th 2009 at 07:20 AM.
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  3. #3
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    Hey Mr. Fantastic,
    Thanks for your help, although I'm still a little confused about how to approach this particular question. Once I have the i term, where do i go from there? Is there any particular formula that i need to use?

    Thanks,
    Function
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  4. #4
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    Quote Originally Posted by function View Post
    Hey Mr. Fantastic,
    Thanks for your help, although I'm still a little confused about how to approach this particular question. Once I have the i term, where do i go from there? Is there any particular formula that i need to use?

    Thanks,
    Function
    You have z^5 = r^5 \text{cis} (5 \theta) = \text{cis} \left( \frac{\pi}{2} + 2n \pi\right) where n is an integer.

    Therefore z = r \text{cis} (\theta) = \text{cis} \left( \frac{\pi}{10} + \frac{2n \pi}{5} \right) .

    Now substitute five consecutive values of n to get the five distinct roots.
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  5. #5
    Senior Member pacman's Avatar
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    Roots in the complex plane,
    z1 = i,
    z2 = (-1)^(9/10),
    z3 = -(-1)^(3/10),
    z4 = -(-1)^(7/10),
    z5 = (-1)(1/10)
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