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Chapter 1 / Re: Past quiz 1
« on: September 20, 2020, 12:09:42 PM »
I disagree. By definition of norm, it is nonnegative. Thus, in order for Re$(z) = |\cdot|$, it has to be nonnegative. You cannot make the first equivalence. For example, $|z| = -3$ is an empty set, although $x^2+y^2=9$ is a circle.