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Math Help - Can someone help me with complex numbers?

  1. #1
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    Help with complex numbers?

    I was doing some complex numbers problems today and something has me really confused. I had to find the arument of -2-2root3i so I plotted the point on an argand diagram and used tan to find the reference angle. Then I added pi to it because thats what the book said to do for the 3rd quadrant in the previous questions and because I thought the argument was the angle between the positive x axis and the line joining the complex number to the origin. I always that it was in an anticlockwise direction. But this time the book said to add -pi and continued to do this for the rest of the questions. Now i am confused as to how i find the argument. Can someone please help.

    Thanks
    Last edited by SahilShet; May 5th 2013 at 07:14 AM.
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  2. #2
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    Re: Can someone help me with complex numbers?

    The "standard" argument for complex numbers lies between 0 and 2\pi while "arctan" always gives a value between -\pi/2 and \pi/2. In the case of -2- 2\sqrt{3} we are looking at arctan(\sqrt{3})= \pi/3 which is ih the first quadrant so we add \pi to get \frac{4\pi}{3}.

    However, the "argument" of a complex number is not "uniquely" defined. Adding or subtracting 2\pi to the argument will give another that is also a valid argument for that same complex number. Subtracting 2\pi from \frac{4\pi}{3}, of course, gives the same as subtracting \pi from \frac{\pi}{3}. As I said before the "standard" is between 0 and 2\pi but there might be good reason to use another representation.
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  3. #3
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    Re: Can someone help me with complex numbers?

    Thanks so much for your answer! It definitely makes more sense now
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