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    I am currently revising for my complex analysis exam on Friday? I can't seem to grasp that idea that
    |z|^4 = x^4 + y^4 +2x^2y^2, this is when z=(x+iy).

    The approach I took to it was doing (x+iy)^2, then from this result (x+iy)^3 and so on, but I have not been able to reach that result. I know it's right as it is given in the mark scheme however I can't get my head around it. Where have all the i's gone to?
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    (Original post by gdickinson_)
    I am currently revising for my complex analysis exam on Friday? I can't seem to grasp that idea that
    |z|^4 = x^4 + y^4 +2x^2y^2, this is when z=(x+iy).

    The approach I took to it was doing (x+iy)^2, then from this result (x+iy)^3 and so on, but I have not been able to reach that result. I know it's right as it is given in the mark scheme however I can't get my head around it. Where have all the i's gone to?
    Why have you squared z? The modulus of a complex number is \sqrt{x^2+y^2}.


    And so |z|^4=(\sqrt{x^2+y^2})^4=(x^2+y^  2)^2=x^4+2x^2y^2+y^4
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    your mistake is that you are doing z^4 whereas the formula is for |z|^4.
    |z| = (x^2 + y^2)^(1/2)
    |z|^2 = (x^2 + y^2)
    |z|^4 = x^4 + y^4 +2x^2y^2
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    (Original post by Kvothe the Arcane)
    Why have you squared z? The modulus of a complex number is \sqrt{x^2+y^2}.


    And so |z|^4=(\sqrt{x^2+y^2})^4=(x^2+y^  2)^2=x^4+2x^2y^2+y^4
    In the pic it should be z=x+iy
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    (Original post by Lychee627)
    In the pic it should be z=x+iy
    Thanks. I've amended
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    Thank you so much everyone!!
 
 
 
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