# Finding the arg equation of arc with given endpoints

• Jan 31st 2013, 04:20 AM
director
Finding the arg equation of arc with given endpoints
Hi guys,

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!
• Jan 31st 2013, 02:41 PM
Prove It
Re: Finding the arg equation of arc with given endpoints
You do realise that "arg" is used to represent the angle that is swept out from the positive x axis in the anticlockwise direction, right?

So you'd be starting at -1 + 0i and going to 1 + 0i, passing through 0 + i. It should be obvious that it's a semicircle centred at the origin of radius 1. How big is the angle in a semicircle?
• Jan 31st 2013, 05:51 PM
director
Re: Finding the arg equation of arc with given endpoints
Thanks, Prove It.

I didn't think about it this way... my brain was fixated on the angle between the line segments from 1 to i and -1 to i.