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    Hi there. I've recently had to self teach myself a bit about complex numbers and only have the internet as a resource. I was wondering if anybody could please explain the modulus-argument form to me seeing as looking around the internet doesnt really provide any explanations for it.

    Thanks in advance for any help.
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    (Original post by Traceur)
    Hi there. I've recently had to self teach myself a bit about complex numbers and only have the internet as a resource. I was wondering if anybody could please explain the modulus-argument form to me seeing as looking around the internet doesnt really provide any explanations for it.

    Thanks in advance for any help.
    The general form is z= r(\mathrm{cos} \theta +i \mathrm{sin} \theta)

    If z is represented in cartesian form, z=x+yi, then r=\sqrt{x^2 +y^2} and \theta = \mathrm{tan}^{-1}\dfrac{y}{x} i.e. r is the modulus of the complex number and the angle is the argument. You may also find that it is sometimes called polar form.
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    Basically, when you write z=r(\cos \theta + i\sin \theta), then r tells you how far the point z is away from the origin, and \theta is the angle (measured anti-clockwise) that the line Oz makes with the positive x-axis.
 
 
 
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Updated: April 2, 2011
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