# Complex Numbers Locus Question

1. Nov 30, 2009

### Amaru58

1. The problem statement, all variables and given/known data
Find the cartesian equation of the locus |z+3+2i|=Re(z)

2. Relevant equations

3. The attempt at a solution
You let z= x +iy
therefore Re(z)=x?

2. Nov 30, 2009

### Hootenanny

Staff Emeritus
Indeed. So you now have

$$x = \left| x + 3 +iy + 2i\right|$$

Can you write that in canonical form?

3. Nov 30, 2009

### Amaru58

OK. I'm not too sure what you mean by canonical form?
Would x = {(x+3)^2 + (y+2)^2}^1/2
Therefore: x^2 = x^2 +6x + 9 +y^2 +4y+4
6x+4y+y^2=-13
I'm not quite sure what to do now
Thanks for the help

4. Nov 30, 2009

### Hootenanny

Staff Emeritus
You're there. The canonical form in Cartesian coordinates is usually f(x,y) = 0 or f(x,y) = const., which is what you have there.