# Complex Numbers Stuff

• Jun 9th 2008, 05:32 AM
Evales
Complex Numbers Stuff
Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

I have never come across this type of question. Any hints on how to tackle it?
• Jun 9th 2008, 05:45 AM
mr fantastic
Quote:

Originally Posted by Evales
Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

I have never come across this type of question. Any hints on how to tackle it?

{z : |z - 1| = 2} ..... The distance of z from 1 is always equal to 2. Geometrically then z lies on a circle of radius 2 and centre at z = 1.

{z : Re z less then or equal to 0} ..... You have the left half of the complex plane (the part to the left of the Im(z) axis).

Put the two together and look for the overlap ......
• Jun 9th 2008, 05:46 AM
bobak
Quote:

Originally Posted by Evales
Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

I have never come across this type of question. Any hints on how to tackle it?

This is a standard problem about loci in the complex plane. Are you familiar with the following ?

• $|z| = r$ describes a circle at the origin of radius r
• $|z- (a +bi)| = r$ describes a circle with centre $(a ,b)$ and radius r
• $|z - (a +bi) | = |z - (c +di) |$ is the perpendicular bisector of the line joining the points $(a ,b)$ and $(c ,d)$

If you know this problem should be very easy, otherwise using the information I gave you attempt the problem and let me know I you have any issues.

Bobak
• Jun 9th 2008, 06:08 AM
Evales
Ahh thanks