MAT334--2020F > Chapter 1

1.2 circles

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Maria-Clara Eberlein:
When we have are asked to find the locus of |z-p|=|z-q|, 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?

shiyuancao:
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.

Lubna Burki:
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).