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# how is |z|^4 = x^4 + y^4 +2x^2y^2 ?! watch

1. 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?
2. (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 .

And so
3. 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
4. (Original post by Kvothe the Arcane)
Why have you squared z? The modulus of a complex number is .

And so
In the pic it should be z=x+iy
5. (Original post by Lychee627)
In the pic it should be z=x+iy
Thanks. I've amended
6. Thank you so much everyone!!

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