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Not certain about Complex Number, Polar Form Question

  1. Mar 16, 2007 #1
    1. The problem statement, all variables and given/known data
    The question:
    a)Solve the equation [tex]z^{3}=4\sqrt{2}-4\sqrt{2}i.[/tex].
    b)Express the answer in polar form.


    3. The attempt at a solution

    Here's what i got:

    [tex]r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8[/tex]
    [tex]\tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}[/tex]
    [tex]z^{3}=8^{3}cis\left(-45\cdot3\right)[/tex]
    [tex]z^{3}=512\left(cos\frac{5\pi}{4}-i\sin\frac{5\pi}{4}\right)[/tex]
    [tex]z^{3}=512\left(\frac{-\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i\right)[/tex]
    [tex]=-256\sqrt{2}+256\sqrt{2}i\right)[/tex]

    im not sure if this is right, im supposed to graph this, and with these kinds of numbers, i figure i went wrong somewhere, i have no idea what they mean by "solve" and how or if this "solves" anything other than the fact that it ends with an equal sign, so if someone can check it for me id appreciate it, thanks."
     
    Last edited: Mar 16, 2007
  2. jcsd
  3. Mar 16, 2007 #2

    mjsd

    User Avatar
    Homework Helper

    i think you are solving for z, so you should have
    [tex]z^{3}=4\sqrt{2}-4\sqrt{2}i=8 cis\left(-45\right)[/tex]
    and then cube root both sides....
    hint: should get 3 roots
     
  4. Mar 17, 2007 #3
    oh, so i went too far, now i see what im supposed to be solving, thanks.
     
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