Author Topic: Quiz 1- Lec 5101-A  (Read 465 times)

Pengyun Li

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Quiz 1- Lec 5101-A
« 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 $z=x+iy$,

$z^2 = (x+iy) (x+iy) = x^2-y^2+(2xy)i$.

Thus, $Re(z^2) = x^2-y^2=4$.

Therefore, the locus of points z is a hyperbola with equation $x^2-y^2=4$.
« Last Edit: September 25, 2020, 03:51:50 PM by Pengyun Li »