# Argand Diagram: Difference in argument = pi/4

#### 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..

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#### LCKurtz

Science Advisor
Homework Helper
Gold Member
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..
If $z=x+yi$ and you call $\theta_1=arg(z-1)$and $\theta_2=arg(z+1)$ what happens if you calculate $\tan(\theta_1-\theta_2)$?

#### Dick

Science Advisor
Homework Helper
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..
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.

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