# Argand Diagram: Difference in argument = pi/4

1. Jun 4, 2013

### unscientific

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

Sketch the locus of points in the argand diagram defined by z:

arg (z-1) - arg(z+1) = ∏/4

2. Relevant equations

3. The attempt at a solution

By simple geometry i worked out that at a point in the x-y plane, the angle subtended from that point to -1 and 1 must be = pi/4.

For a circle I know this must be = pi/2. But for pi/4 I have no clue..

2. Jun 4, 2013

### LCKurtz

If $z=x+yi$ and you call $\theta_1=arg(z-1)$and $\theta_2=arg(z+1)$ what happens if you calculate $\tan(\theta_1-\theta_2)$?

3. Jun 4, 2013

### Dick

I know that it's a different circle, but that's for me you know and you to find out after you put some work in on this. How do you know pi/2 defines a circle? Apply the same ideas.