Toronto Math Forum
MAT3342020F => MAT334Lectures & Home Assignments => Chapter 1 => Topic started by: MariaClara Eberlein on September 23, 2020, 07:27:50 PM

When we have are asked to find the locus of zp=zq, can we immediately say the perpendicular bisector of the line segment joining p and q, or must we plug in z=x+iy and solve to get x=0?

I think this depends on how you want to represent your solution. Both of them seems rational to me.
But $x$ does not necessarily to be $0$ since $p$ and $q$ are some arbitrary complex numbers.

I think it's enough to say that this looks like one of the Apollonius circles in which is row is 1 then a line is given (specifically the perpendicular bisector of the two foci).