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    melissa816's Avatar
    melissa816 Posts: 1, Reputation: 1
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    #1

    Dec 11, 2006, 04:29 PM
    Complex numbers and nth roots
    Using De Moivre's theorem and nth roots of complex numbers I need help putting z= the square root of 3 + I in trig form then finding the 5th roots of z and how to graph the roots.
    Can you answer this?
    asterisk_man's Avatar
    asterisk_man Posts: 476, Reputation: 32
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    #2

    Dec 12, 2006, 06:28 AM
    http://en.wikipedia.org/wiki/De_Moivre's_formula seems like a good source of info on De Moivre's formula.

    First you need to convert z=3+i into polar form. Look here: http://en.wikipedia.org/wiki/Polar_c...an_coordinates

    Graphing the result should be easy. Your answer should be a complex number, graph the point with the real part as the x coordinate and the imaginary part as the y coordinate.

    Ask any questions if you don't understand something or want someone to review what you have done.
    Thanks!
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #3

    Dec 12, 2006, 06:32 AM
    Complex coordinates are delicious! Mmmm!
    Elisha Grey's Avatar
    Elisha Grey Posts: 31, Reputation: 0
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    #4

    Jan 18, 2007, 10:56 AM
    z = 3 + I = sqrt (10) e^(I arc tan(1/3)) = 10^(1/2) e^(I arc tan(1/3)), so sqrt z =
    10^(1/4) e^(I(1/2)arc tan(1/3)).
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