<s>[INST] representation of a complex number in polar from 
Write the following in polar form: $\frac{1+\sqrt{3}i}{1-\sqrt{3}i}$

$$\frac{1+\sqrt{3}i}{1-\sqrt{3}i}=\frac{1+\sqrt{3}i}{1-\sqrt{3}i}\cdot\frac{1+\sqrt{3}i}{1+\sqrt{3}i}=\frac{(1+\sqrt{3}i)^2}{1^2+(\sqrt{3})^2}=\frac{1+2\sqrt{3}i-3}{4}=\frac{-2+2\sqrt{3}i}{4}=-\frac{1}{2}+\frac{\sqrt{3}}{2}i$$
$|z|=r=\sqrt{(-\frac{1}{2})^2+(\frac{\sqrt{3}}{2})^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=1$
arg$z$=$tan^{-1}(\frac{\sqrt{3}}{2}\cdot -2)=-\frac{\pi}{3}$
acorrding to Wolfram $\theta=0$
 [/INST] You forget the brackets in your wolfram formula, the correct one is this and as you can see your result is correct. 
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