I'm kind of struggling to understand the ARG representation of a (complex) arc maybe if I can see a properly solved example, it'll be become clearer.

Problem: find an ARG equation for the arc with end points \(\displaystyle -1\) and \(\displaystyle 1\) passing through \(\displaystyle i\).

The equation is in the form

**arg[(z - A) / (z - B)] = Theta**

Taking \(\displaystyle z = i\), \(\displaystyle A = -1\), B = 1

I get agr[(i + 1) / (i - 1)] = -PI/2

I suppose this makes sense that the angle is 90 deg. Is this right?

Then how do I present the final equation of this arc?

**arg[(z - A) / (z - B)] = -PI/2 ...............?**

How do I manipulate the equation to find some other point on this arc besides the three already given?

Thanks!