# Math Help - Complex Numbers Stuff

1. ## 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?

2. 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 ......

3. 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

4. Ahh thanks