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# small question on argand diagram with negative real numbers watch

1. 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 .

So I did what I usually do and turned it into

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

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,
2. 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 .
3. 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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