Quiz1-6101 A

[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 $|x+iy-1|$