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Math Help - Find All Complex Roots

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    Find All Complex Roots

    Find all complex roots. Leave your answers in polar form with the argument in degrees.

    (1) The complex fourth roots of sqrt{3} - i.


    (2) The complex firth roots of -i.
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    Quote Originally Posted by magentarita View Post
    Find all complex roots. Leave your answers in polar form with the argument in degrees.

    (1) The complex fourth roots of sqrt{3} - i.


    (2) The complex firth roots of -i.
    Reading this might help: Complex numbers : De Moivre's theorem : De Moivre's theorem and nth roots

    You might also find this helpful: http://shawtlr.net/trig/trig_m11_slides.pdf
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    Quote Originally Posted by magentarita View Post
    Find all complex roots. Leave your answers in polar form with the argument in degrees.

    (1) The complex fourth roots of sqrt{3} - i.


    (2) The complex firth roots of -i.
    1) \sqrt{3} - i = | \sqrt{3} - i | e^{i \arg (\sqrt{3} - i)} = 2 e^{-i\pi/6}.

    Therefore, the fourth roots are: 2^{1/4} e^{-\pi i/24}, -2^{1/4} e^{-\pi i/24}, i2^{1/4}e^{-\pi i/24}, -i 2^{1/4} e^{-\pi i/24}.

    2) -i = e^{-\pi i /2}.

    Therefore, the fifth roots are: e^{-\pi i/10}, \zeta e^{-\pi i/10}, \zeta^2 e^{-\pi i/10}, \zeta^3 e^{-\pi i/10}, \zeta^4 e^{-\pi i/10}.

    Where \zeta = e^{2\pi i/5}
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    Thanks but.....

    Quote Originally Posted by ThePerfectHacker View Post
    1) \sqrt{3} - i = | \sqrt{3} - i | e^{i \arg (\sqrt{3} - i)} = 2 e^{-i\pi/6}.

    Therefore, the fourth roots are: 2^{1/4} e^{-\pi i/24}, -2^{1/4} e^{-\pi i/24}, i2^{1/4}e^{-\pi i/24}, -i 2^{1/4} e^{-\pi i/24}.

    2) -i = e^{-\pi i /2}.

    Therefore, the fifth roots are: e^{-\pi i/10}, \zeta e^{-\pi i/10}, \zeta^2 e^{-\pi i/10}, \zeta^3 e^{-\pi i/10}, \zeta^4 e^{-\pi i/10}.

    Where \zeta = e^{2\pi i/5}
    Thanks but your reply is far beyond precalculus. All my questions come a precalculus textbook that I am studying in preparation for a state test.

    What does your reply mean? What do all those symbols mean?

    Thanks
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