I need to take a raincheck with this problem. I want to make sure I haven't messed up some fundamental idea.
Convert the complex number $-\dfrac{1}{2} + \dfrac{\sqrt3}{2}i$ to polar form.
I took the modulus as below,
$\lvert-\dfrac{1}{2} + \dfrac{\sqrt3}{2}i \rvert = \sqrt{(\dfrac{-1}{2})^2 + (\dfrac{\sqrt 3}{2})^2} = 1$
And the argument as below,
$arg(-\dfrac{1}{2} + \dfrac{\sqrt3}{2}i) = \tan^{-1} (\dfrac{\sqrt 3}{2} \times \dfrac{-2}{1}) = -60 = -\dfrac{\pi}{3}$
Hence the complex number in polar form is,
$-\cos \dfrac{\pi}{3} + i \sin \dfrac{\pi}{3}$
But, The required answer is $\cos \dfrac{2\pi}{3} + i \sin \dfrac{2\pi}{3}$
I thought of converting the -60 to positive, as 360 - 60 = 300, ie:- $\dfrac{5\pi}{3}$. I have a feeling I am missing something important. Can you guys tell me where I am going wrong? Thanks for all your help!