Toronto Math Forum
MAT334--2020F => MAT334--Tests and Quizzes => Quiz 1 => Topic started by: Pengyun Li on September 24, 2020, 07:06:24 PM
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$\textbf{Question:}$ Describe the locus of points z satisfying the given equation: $Re(z^2) = 4$.
$\textbf{Answer:}$
Let $z=x+iy$,
$z^2 = (x+iy) (x+iy) = x^2-y^2+(2xy)i$.
Thus, $Re(z^2) = x^2-y^2=4$.
Therefore, the locus of points z is a hyperbola with equation $x^2-y^2=4$.