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Math Help - Complex number algebra question

  1. #1
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    Complex number algebra question

    Hi, can someone please verify my answers to this question. Thanks heaps!!

    Find all complex numbers w and z satisfying:

    1/w + 1/z = 1/wz and 2wz - z^2 -1 = 0


    - I got the answers z = 1/3 +(or)- (√2 / 3) i and w = 2/3 + (or) - (√2 / 3)i
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  2. #2
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    Re: Complex number algebra question

    You are absolutely right.
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  3. #3
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    Re: Complex number algebra question

    Yea correct.
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  4. #4
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    Re: Complex number algebra question

    Could someone please show me how you get this answer?
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  5. #5
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    Re: Complex number algebra question

    Complex number algebra question-complex-13-mar.png
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  6. #6
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    Re: Complex number algebra question

    Multiply both sides of \frac{1}{z}+ \frac{1}{w}= \frac{1}{wz} by wz to get w+ z= 1. Then w= 1- z so the second equation becomes 2wz - z^2 -1= 2(1- z)z- z^2- 1= 2z- 2z^2- z^2- 1= -3z^2+ 2z- 1 = 0 which the same as 3z^2- 2z+ 1= 0. Use the quadratic formula, or complete the square, to solve that for z
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