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Math Help - Roots of complex numbers

  1. #1
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    Roots of complex numbers

    Hello,

    I need to find the relationship bewteen the power (n) in the equation : Z^n = a+bi , where |a+bi|=1 ...is it possible ? (Something other than De Moiver's theorem).

    Thanks.
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  2. #2
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    I need to find the relationship bewteen the power (n) and what?
    You do not have a compete thought there.
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  3. #3
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    Re: Roots of complex numbers

    Oh sorry , I missed that :

    the relation bewteen the power (n) in the equation : Z^n = a+bi and the roots of Z (Solutions to the equation) , where |a+bi|=1 .... I need a general pattern relating them.
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  4. #4
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    the relation bewteen the power (n) in the equation : Z^n = a+bi and the roots of Z (Solutions to the equation) , where |a+bi|=1 .... I need a general pattern relating them.
    1) there are n distinct complex numbers that satisfy that equation.

    2) each one is point on the unit circle.

    3) they create n arcs of equal measure, \frac{2\pi}{n}.
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    Re: Roots of complex numbers

    and there's no other mathematical relationship or pattern between them?
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    and there's no other mathematical relationship or pattern between them?
    Why don't you investigate that?

    Start with looking at the sum of the roots.
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  7. #7
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    Re: Roots of complex numbers

    so if I started with adding the roots of an equation of Z^n=a+bi , where |a+bi|=1 .... I wil lbe able to fing a pattern?
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    so if I started with adding the roots of an equation of Z^n=a+bi , where |a+bi|=1 .... I wil lbe able to fing a pattern?
    No comment. Sorry
    Do you know anything about this topic?
    If so, please tell us what you know, in detail, so we can truly help you.
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  9. #9
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    Re: Roots of complex numbers

    aha ... but do you mean with "no comment" taht there is no known pattern for this ... or you want me to show my work I done first ?
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    aha ... but do you mean with "no comment" taht there is no known pattern for this ... or you want me to show my work I done first ?
    Start thinking about the help you've been given and doing something instead of just fishing for more help.
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  11. #11
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    Re: Roots of complex numbers

    Quote Originally Posted by Hyunqul View Post
    Hello,

    I need to find the relationship bewteen the power (n) in the equation : Z^n = a+bi , where |a+bi|=1 ...is it possible ? (Something other than De Moiver's theorem).

    Thanks.
    Asked here: http://www.mathhelpforum.com/math-he...de-187045.html

    Thread closed.
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