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Math Help - Complex equation

  1. #1
    Pim
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    Complex equation

    iz^2-z+i=0
    Are there solutions to this equation? If yes, how could I calculate it/them?
    This was a question on a test I had and I suspect it was a typo, though I still would like to know how to solve it.

    I tried multiplying by -i, this gives:
    z^2+zi+1=0
    But I can't see how I could factorise this.

    Thanks in advance.
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  2. #2
    A Plied Mathematician
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    By the Fundamental Theorem of Algebra, this equation has two complex roots. They might be repeated, but there is definitely a solution. I would use the quadratic formula. It's still valid even when the coefficients are complex.
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  3. #3
    Pim
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    Ah, yes, I see. For anyone who's wondering, the roots are (\frac{1}{2}+\frac{1}{2}\sqrt{5})i and (\frac{1}{2}-\frac{1}{2}\sqrt{5})i

    Thanks a lot!
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  4. #4
    A Plied Mathematician
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    You're very welcome. Have a good one!
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  5. #5
    A Plied Mathematician
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    I think your roots are the opposite sign of what they should be. I would double-check them.
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