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Math Help - Complex numbers - equations

  1. #1
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    Complex numbers - equations

    Hello everybody

    I need someone to check whether my results are correct or incorrect:

    Equation:

    z2=1-i


    My results are attached as an image. I think the results are wrong but the problems is that I've used the correct method. it would be really nice if someone could tell me whether the results are correct or incorrect.

    Thank you
    Attached Thumbnails Attached Thumbnails Complex numbers - equations-billede-2.png  
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  2. #2
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    Re: Complex numbers - equations

    Quote Originally Posted by Tala View Post
    Equation: z2=1-i
    I think the results are wrong but the problems is that I've used the correct method. it would be really nice if someone could tell me whether the results are correct or incorrect.
    When you say "I've used the correct method", what do you mean?

    One root is \sqrt[4]2\exp\left(\frac{-\pi i}{8}\right)~, where \exp(it)=\cos(t)+i\sin(t).
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  3. #3
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    Re: Complex numbers - equations

    This is what I've done:
    Attached Thumbnails Attached Thumbnails Complex numbers - equations-billede-1.png   Complex numbers - equations-billede-2.png  
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Complex numbers - equations

    I would write:

    z^2=1-i=\sqrt{2}\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i \right)=\sqrt{2}e^{\left(\frac{7\pi}{4} \right)i}

    Hence:

    z=\pm\sqrt[4]{2}e^{\left(\frac{7\pi}{8} \right)i}

    Now you may use Euler's formula to find the rectangular form.
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  5. #5
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    Re: Complex numbers - equations

    Quote Originally Posted by Tala View Post
    This is what I've done:
    Those are correct.
    But where did you get the numbers in the OP?
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  6. #6
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    Re: Complex numbers - equations

    I just multiplied...
    Attached Thumbnails Attached Thumbnails Complex numbers - equations-billede-4.png  
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Complex numbers - equations

    Did you use software or half-angle identities to evaluate the trig. functions?
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  8. #8
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    Re: Complex numbers - equations

    Software...But are my results correct ?
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  9. #9
    MHF Contributor MarkFL's Avatar
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    Re: Complex numbers - equations

    Yes, they are correct.
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