Toronto Math Forum
MAT3342020F => MAT334Lectures & Home Assignments => Chapter 1 => Topic started by: ziyizhou on September 23, 2020, 04:34:40 PM

Sketch the locus of those points 𝑤 with
w+2=w2

could you please show the step?

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 yaxis bisects the line segment between (2,0) and (2,0).

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=(x2)+iy. Then take the square of both sides and organize the equation. Finally you will get x=0, which is the yaxis.
The second way to do this problem is to illustrate it geometrically. w+2 = w2 is same as w(2)=w2, 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 yaxis.