# Toronto Math Forum

## MAT334--2020F => MAT334--Tests and Quizzes => Quiz 1 => Topic started by: Jingyu Zhang on September 24, 2020, 01:22:36 PM

Title: Quiz1-6101 A
Post by: Jingyu Zhang on September 24, 2020, 01:22:36 PM
Question: Describe the locus of points z satisfying the given equation:
|z-i|=Re z
Ans:
for z = x+ iy
|x+iy-1|=Re(x+iy)
|x+i(y-1)|=x
x^2+(y-1)^2=x^2
(y-1)^2=0
y= 1
Therefore, the locus is a horizontal line.
Title: Re: Quiz1-6101 A
Post by: shiyuancao on September 24, 2020, 04:19:59 PM
Hi, there might be a typo in second line of your answer.

Title: Re: Quiz1-6101 A
Post by: Jiaqi Bi on December 20, 2020, 01:08:17 PM
The second line of the answer, left part of your equation should be $|x+iy-i|$ instead of $|x+iy-1|$