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Math Help - solution to the equation (complex roots)

  1. #1
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    solution to the equation (complex roots)

    I normally have no problem solving simple equations iand finding there complex roots but Could someone please help me solve this problem as the equation looks really nasty:

    solution to the equation (complex roots)-untitled.jpg

    Thank you

    Ps: I not sure if this problem is in the right section
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  2. #2
    Junior Member nimon's Avatar
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    Simply rearrange your equation to give

    z-\frac{i}{2} = (-i)^{\frac{1}{3}},

    then so long as you can find the third roots of -i you can solve for z.

    Write back if you need any help finding the third roots,

    Cheers
    Last edited by nimon; January 16th 2010 at 11:42 AM. Reason: tex went skewiff!
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  3. #3
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    Quote Originally Posted by nimon View Post
    Simply rearrange your equation to give

    z-\frac{i}{2} = (-i)^{\frac{1}{3}},

    then so long as you can find the third roots of -i you can solve for z.

    Write back if you need any help finding the third roots,

    Cheers
    Thanks for the start i managed to do this but how would i got stuck after this.
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  4. #4
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    The three cube roots of -i are:
    \text{cis}\left(\frac{-\pi}{6}\right)~,~\text{cis}\left(\frac{\pi}{2}\rig  ht)~\&~\text{cis}\left(\frac{-5\pi}{6}\right).
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  5. #5
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    Thanks for the help, i can know finish the problem help off.
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