Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 1 => Topic started by: Pengyun Li on September 24, 2020, 07:06:24 PM

$\textbf{Question:}$ Describe the locus of points z satisfying the given equation: $Re(z^2) = 4$.
$\textbf{Answer:}$
Let $z=x+iy$,
$z^2 = (x+iy) (x+iy) = x^2y^2+(2xy)i$.
Thus, $Re(z^2) = x^2y^2=4$.
Therefore, the locus of points z is a hyperbola with equation $x^2y^2=4$.