MAT334--2020F > Quiz 1

Quiz 1- Lec 5101-A

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Pengyun Li:
$\textbf{Question:}$ 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 $x^2-y^2=4$.