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 $|x+iy-1|$