What does $\arg(z-z_1)-\arg(z-z_2)=\phi$ represents.
where $z$ is point in argand plane
My Doubt:
I am attaching a Image for the doubt because I don't know How to draw in latex. I'll be grateful if you can tell me how to do that.
I am considering $z_1$ is right of $z_2$
I've drawn $4$ diagram for locus. Can you tell me Are the arrow marked for angle by me are correct?
Also you can give me more information If you have.
Also locus of $z$ will be full circle or half circle if $\phi$ is $\dfrac{\pi}{2}$. If it is full circle what will be arrow mark for angle.
Best Answer
I am adding My Own Answer
Here I'm Attaching two Images in which I've plotted Locus of $z$ because I don't know how to plot them Digitally. Arrow Must end at $(z-z_1)$ and must originate from $z-z_2$.
Also I am considering Principle Argument that is $(-\pi,\pi]$.![enter image description here](https://i.stack.imgur.com/2Kv05.jpg)