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small question on argand diagram with negative real numbers watch

    • Thread Starter
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    I was doing a question earlier and one step in the question involved going from a complex number in the form (x+yi) to the exponential form. The number was a real number, just -2\sqrt2.

    So I did what I usually do and turned it into 2^\frac{3}{2}e^0

    After discovering my answer didn't match the model answer it became clear my conversion should have given

    2^\frac{3}{2}e^i^\pi

    since the number was negative and so at a 180degree angle to the positive real axis on the argand diagram.

    Anyway, I'm just wondering if I was going about things in the right way by remembering that it should be pi and not 0 by visualizing the argand diagram or if there is instead a mathematical method of getting the right answer instead of zero for a negative answer.

    thanks,
    • PS Helper
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    If you draw a line from the origin to your complex number, the argument of the complex number tells you the angle that the line you drew makes with the positive x-axis (that is, the line starting at the origin and going off to the right), measured anti-clockwise. So positive real numbers have argument 0, and negative real numbers have argument \pi.
    • Community Assistant
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    If you visualise things on an argand diagram, it's hard to go wrong!
    Eventually it'll become second nature to do a mental check to see if you answer in the exponential form is logical (correct quadrant/modulus and so on)
 
 
 
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Updated: April 12, 2011

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