Express $1 + \sqrt{3}\,i$ in polar form.
A$2(\cos 30^\circ + i\sin 30^\circ)$
B$2(\cos 60^\circ + i\sin 60^\circ)$CORRECT
C$4(\cos 60^\circ + i\sin 60^\circ)$
D$\sqrt{2}(\cos 60^\circ + i\sin 60^\circ)$
JUPEBMathematicsComplex Numbers
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Why the answer is B, and why the others tempt you.
The modulus is $\sqrt{1 + 3} = 2$ and the argument is $\tan^{-1}\left(\dfrac{\sqrt{3}}{1}\right) = 60^\circ$, so the polar form is $2(\cos 60^\circ + i\sin 60^\circ)$. Using $30^\circ$ comes from computing $\tan^{-1}\left(\dfrac{1}{\sqrt{3}}\right)$, and 4 is the modulus squared.
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