# Toronto Math Forum

## MAT334--2020F => MAT334--Tests and Quizzes => Quiz 1 => Topic started by: xuanzhong on September 25, 2020, 07:44:43 PM

Title: quiz 1 5101
Post by: xuanzhong on September 25, 2020, 07:44:43 PM
Find the locus of points for:
$$Re(z^{2}) = 4$$
$$Let z=x+iy$$
$$Re((x+iy)^{2}) = 4$$
$$Re(x^{2}+2ixy-y^{2}) = 4$$
$$x^{2} - y^{2} = 4$$
$$\frac{x^{2}}{4} - \frac{y^{2}}{4} = 1$$
Therefore, the locus of z is a hyperbolic curve with $\frac{x^{2}}{4} - \frac{y^{2}}{4} = 1$