Complex Numbers help

1. Feb 10, 2013

kiwi101

1. The problem statement, all variables and given/known data

Sketch the line described by the equation:
|z − u| = |z|

z = x+jy
u = −1 + j√3

3. The attempt at a solution

(x+1)^2 + j(y-√3)^2 = (x+jy)^2

I just don't quite get where to go with this

2. Feb 10, 2013

Dick

|z|^2=(x^2+y^2). There is no j in there. There shouldn't be any j in the left hand side either. It's an absolute value.

3. Feb 10, 2013

kiwi101

oh yeah
and um did you mean |z|^2=(x+y)^2?

4. Feb 10, 2013

Dick

Definitely not! |z|=sqrt(x^2+y^2). Look it up.

5. Feb 10, 2013

Staff: Mentor

If z = x + iy, then |z|2 = x2 + y2, which is what Dick wrote. kiwi101, it looks like you need to review the definition of the absolute value or magnitude of a complex number.

6. Feb 10, 2013

kiwi101

I was just about to write a long argument about how I was right and then I realized you're right. I misinterpreted something.

So this is what I have done, I feel its right.

(x+1)^2 + (y-√3)^2 = x^2 + y^2

x^2 + 2x + 1 + y^2 -2√3y + 3 = x^2 + y^2

2x + 1 -2√3y + 3 = 0

(x+2)/√3 = y

and then rationalize it and this is the equation of the line?

7. Feb 10, 2013

Dick

That looks ok to me.

8. Feb 10, 2013

kiwi101

Thanks!
Out of curiousity this question:

Sketch the line or curve described by the equation
ℜe{z} + ℑm{z} = ℜe{u}

would be x + jy = -1 ?

so is this a line or what?

9. Feb 10, 2013

kiwi101

Wait do I solve for y and then rationalize like

y = (-1 -x)/j

10. Feb 10, 2013

Dick

Im(z)=y, not jy. Check the definition again.

11. Feb 10, 2013

kiwi101

I just assumed that since it says Im(z) it meant to include the imaginary iota.

So then I guess it is just a line y = -1-x

12. Feb 10, 2013

Dick

Yep!

13. Feb 10, 2013

kiwi101

Thanks once again! :)