Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 1 => Topic started by: xuanzhong on September 25, 2020, 07:44:43 PM

Find the locus of points for:
$$
Re(z^{2}) = 4
$$
$$
Let z=x+iy
$$
$$
Re((x+iy)^{2}) = 4
$$
$$
Re(x^{2}+2ixyy^{2}) = 4
$$
$$
x^{2}  y^{2} = 4
$$
$$
\frac{x^{2}}{4}  \frac{y^{2}}{4} = 1
$$
Therefore, the locus of z is a hyperbolic curve with $\frac{x^{2}}{4}  \frac{y^{2}}{4} = 1$