MAT334--2020F > Quiz 1

Quiz1-6101 A

(1/1)

Jingyu Zhang:
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.

shiyuancao:
Hi, there might be a typo in second line of your answer.

Jiaqi Bi:
The second line of the answer, left part of your equation should be $|x+iy-i|$ instead of $|x+iy-1|$