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Math Help - Finding the arg equation of arc with given endpoints

  1. #1
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    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 -1 and 1 passing through i.

    The equation is in the form arg[(z - A) / (z - B)] = Theta

    Taking z = i, 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!
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  2. #2
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    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?
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  3. #3
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    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.
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