Math CentralQuandaries & Queries


Question from Dylan, a student:


My problem is to prove:

|z|^2 = zz* Where z is the complex number x + iy and z* is it's complex conjugate x - iy.

If the absolute value of i is 1, then it looks like: |z|^2 = |x+y| |x+y| = x^2 + 2xy + y^2

And zz* = x^2 + y^2. for these to be equal, 2xy = 0. This seems wrong to me. What am I doing wrong?


Are you sure that |z|2 = |x+y| |x+y| = x2 + 2xy + y2? Isn't the length of 3 + 4i equal to SQRT (32 + 42) = 5 by Pythagoras' Theorem?



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