Complex Numbers Locus Question

[Amaru58]

Homework Statement

Find the cartesian equation of the locus |z+3+2i|=Re(z)

Homework Equations

The Attempt at a Solution

You let z= x +iy
therefore Re(z)=x?

 

[Hootenanny]

Homework Statement

Find the cartesian equation of the locus |z+3+2i|=Re(z)

Homework Equations

The Attempt at a Solution

You let z= x +iy
therefore Re(z)=x?

Indeed. So you now have

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

Can you write that in canonical form?

 

[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

 

[Hootenanny]

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

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.