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Math Help - trigonometric form and DeMoivres Theorem

  1. #1
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    trigonometric form and DeMoivres Theorem

    list the 3 complex roots of -1 by rewriting -1 in trogonometric form and applying DeMoivre's Theorem. you may leave your answers in trigonometris form
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  2. #2
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    Quote Originally Posted by kenzie103109 View Post
    list the 3 complex roots of -1 by rewriting -1 in trogonometric form and applying DeMoivre's Theorem. you may leave your answers in trigonometris form

    z^3=-1=cis(\pi+2k\pi)=cis(\pi(2k+1))\,,\,\,with\,\,\,ci  s(x):=e^{xi}\,,\,\,x\in\mathbb{R}\,,\,\,k\in\mathb  b{Z} . In order to get all the different elements though we restrict k=0,1,2 (why? Check the trigonometric circle).

    So z=(-1)^{1/3}=cis(\pi(2k+1))^{1/3}=cis\left(\pi\frac{2k+1}{3}\right) (here we used De Moivre's theorem) , so now just input k=0,1,2 and obtain the three complex roots of -1 ...as simple as that!

    Tonio
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