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Argand Diagram: Difference in argument = pi/4

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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..
 

LCKurtz

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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

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Homework Helper
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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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