Perpendicular bisector line equation on complex plane

LongLifeLearner

New member
Joined
Oct 23, 2020
Messages
15
The question asked to write an equation of the perpendicular bisector of the line segment joining -1-3i and 2-i in term of z , specifically in the form of Im ((a+bi)z)=c

by wrote into:
|z-(-1-3i)|=|z-(2-i|
And solve it accordingly i get
3x+2y=-5/2

Knowing the answer is Im((2+3i)z)=-5/2
But i m still struggle to find out what is the principle behind.

Hope someone can assist me the easy way to identify an equation, how to write an equation on complex plane in the form either in Re((a+bi)z) or Im((a+bi)z) especially when involved 2 points, or a point with a known slope. Thanks in advance
 
Top