Sketching complex plane

**SyNtHeSiS** · October 18th 2010, 02:30 PM

Sketch the subset of the complex plane:

{z E C: |z - 1| = |z - i| }

I have no idea what to do. Could someone please explain?

**Archie Meade** · October 18th 2010, 03:10 PM

Originally Posted by SyNtHeSiS

Sketch the subset of the complex plane:

{z E C: |z - 1| = |z - i| }

I have no idea what to do. Could someone please explain?

The modulus of a complex number is it's distance from the origin in the complex plane.
Pythagoras' theorem calculates the distance.

$z=x+iy$

$z-1=(x-1)+iy\Rightarrow\ |z-1|=\sqrt{(x-1)^2+y^2}=\sqrt{x^2+y^2-2x+1}$

$z-i=x+i(y-1)\Rightarrow\ |z-i|=\sqrt{x^2+(y-1)^2}=\sqrt{x^2+y^2-2y+1}$