Toronto Math Forum
MAT3342020S => MAT334Tests and Quizzes => Quiz 1 => Topic started by: Jiayue Wu on February 12, 2020, 05:29:12 PM

Question: Describe the locus of points z satisfying the given equation
$$z1^2 = z+1^2 +6$$
Answer:
$$z=x+iy$$
$$z1 = (x1)+iy$$
$$z+1 = (x+1)+iy$$
$$z1^2 = z+1^2+6 \implies (x1)^2+y^2 = (x+1)^2 + y^2 +6$$
$$4x=6\implies x = \frac{3}{2}\\ z= \frac{3}{2}+iy, y\in \mathbb{R}$$
The locus of points z: z is a verticle line with $x = \frac{3}{2}$