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Math Help - complex numbers-exponential form and solving equations

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    complex numbers-exponential form and solving equations

    1) a) Write -8 in exponential form.
    b) Solve the equation z^4 = −8. (give your answers with real and imaginary parts).
    2) Solve z^3 = 1 + i (leave your answers in the trigonometric form)
    3) Solve z^2 = (√3) − i. (give your answers with real and imaginary parts).
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    Re: complex numbers-exponential form and solving equations

    Quote Originally Posted by heejenna55 View Post
    1) a) Write -8 in exponential form.
    b) Solve the equation z^4 = −8. (give your answers with real and imaginary parts).
    2) Solve z^3 = 1 + i (leave your answers in the trigonometric form)
    3) Solve z^2 = (√3) − i. (give your answers with real and imaginary parts).
    Here is basic help.
    Let \exp(i\theta)=\cos(\theta)+i\sin(\theta).
     - 8 = 8\exp \left( {\pi i} \right)

    1 + i = \sqrt 2 \exp \left( {\frac{{\pi i}}{4}} \right)

    \sqrt 3  - i = 2\exp \left( {\frac{{-\pi i}}{6}} \right)
    Last edited by Plato; September 5th 2013 at 02:11 PM.
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