# Toronto Math Forum

## MAT334--2020F => MAT334--Lectures & Home Assignments => Chapter 1 => Topic started by: Zhekai Pang on September 19, 2020, 11:17:42 PM

Title: Past quiz 1
Post by: Zhekai Pang on September 19, 2020, 11:17:42 PM
http://forum.math.toronto.edu/index.php?topic=1278.0

Why is it a whole line? I also think Re$(z) \geq 0$ is required because the original equation is Re$(z) = | \cdot|$.
Title: Re: Past quiz 1
Post by: RunboZhang on September 20, 2020, 09:59:52 AM
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.