### Author Topic: how to solve this problem?  (Read 1119 times)

#### ziyizhou

• Newbie
• • Posts: 4
• Karma: 0 ##### how to solve this problem?
« on: September 23, 2020, 04:34:40 PM »
Sketch the locus of those points 𝑤 with
|w+2|=|w-2|

#### ziyizhou

• Newbie
• • Posts: 4
• Karma: 0 ##### Re: how to solve this problem?
« Reply #1 on: September 23, 2020, 04:35:24 PM »
could you please show the step?

#### Jessica Long

• Jr. Member
•  • Posts: 6
• Karma: 0 ##### Re: how to solve this problem?
« Reply #2 on: September 23, 2020, 06:03:07 PM »
This is my solution to the problem. Note that the result can also be derived from the Apollonius circle formula with 𝜌=0, since the y-axis bisects the line segment between (2,0) and (-2,0).

#### RunboZhang

• Sr. Member
•    • Posts: 51
• Karma: 0 ##### Re: how to solve this problem?
« Reply #3 on: September 23, 2020, 06:07:15 PM »
I think there are two ways to solve this problem.

Firstly, you can substitute w by x+iy into the equation. Then organize the equation and put real parts together and imaginary parts together. Now you will have the equation |(x+2)+iy|=|(x-2)+iy|. Then take the square of both sides and organize the equation. Finally you will get x=0, which is the y-axis.

The second way to do this problem is to illustrate it geometrically. |w+2| = |w-2| is same as |w-(-2)|=|w-2|, and it asks you to find all w in complex plane that has equal distances to (2,0) and (-2,0). Thus the answer will be the perpendicular bisector of (2,0) and (-2,0), which is still the y-axis.