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Math Help - complex number polar form

  1. #1
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    complex number polar form

    how do I write -8i in polar form?
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  2. #2
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    Quote Originally Posted by tim_mannire View Post
    how do I write -8i in polar form?

    As -i=cis(3\pi/2)=e^{3\pi i/2} , -8i=8e^{3\pi i/2}

    Tonio
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  3. #3
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    z^3 = -8i . Does the polar form change for z^3 = -8i
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  4. #4
    Junior Member raheel88's Avatar
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    Solving z^3 = -8i...so u want to solve for z right?

    If you write z as z = re^{i\theta} and substitute this into z^3 = -8i and solve.

    You get r = 2 and 3\theta = \frac{3\pi}{2} + 2k\pi , (k=0,1).

    Therfore \theta = \frac{\pi}{2} + \frac{2k\pi}{3} , (k=0,1,2)
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  5. #5
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    Quote Originally Posted by raheel88 View Post
    Solving z^3 = -8i...so u want to solve for z right?

    If you write z as z = re^{i\theta} and substitute this into z^3 = -8i and solve.

    You get r = 2 and 3\theta = \frac{3\pi}{2} + 2k\pi , (k=0,1).

    Therfore \theta = \frac{\pi}{2} + \frac{2k\pi}{3} , (k=0,1,2)
    Thanks, however i am just after the polar form for -8i
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  6. #6
    Junior Member raheel88's Avatar
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    Quote Originally Posted by tim_mannire View Post
    Thanks, however i am just after the polar form for -8i
    that's what tonio has posted.

    the polar form doesn't change for z^3 but there are more solutions for z.
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