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Math Help - HorribleArgand Diagram Question

  1. #1
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    HorribleArgand Diagram Question

    Hey,
    i have a question.

    "the roots of a certain equation, when plotted on an argand diagram, represent the vertices of a square. one vertex has a modulus of 2 and an argument of PI/3 (3.1415/3).

    Find the original equation and the three remaining vertices."

    Any help would be much appreciated,
    Ned
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
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    Taguig City, Philippines
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    Quote Originally Posted by Ned Hunter View Post
    Hey,
    i have a question.

    "the roots of a certain equation, when plotted on an argand diagram, represent the vertices of a square. one vertex has a modulus of 2 and an argument of PI/3 (3.1415/3).

    Find the original equation and the three remaining vertices."

    Any help would be much appreciated,
    Ned
    note that if you have a complex number \, z = w^n \, and you want to find all its n roots, then

    w_k = r^{\frac{1}{n}} \, cis (\frac{\theta + 2k\pi}{n})
    where k=0,1,...,n-1

    you can use this fact to find what you want..
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  3. #3
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    Aug 2007
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    thank you. i actually worked it out about 5 minutes after i posted, using that formula that i had already, i was just getting stuck fiddling around with the 2pik

    Cheers
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