The complex number $$ z $$ is given by $$ =\sqrt{3}+i $$, what is the polar representation of $$ z $$ ? Select one: a. $$ \quad \sqrt{2}\left(\cos \left(\frac{\pi}{6}\right)+i \sin \left(\frac{\pi}{6}\right)\right) $$ b. $$ \quad \sqrt{2}\left(\cos \left(\frac{\pi}{6}\right)-i \sin \left(\frac{\pi}{6}\right)\right) $$ c. $$ \quad 2\left(\cos \left(\frac{\pi}{6}\right)-i \sin \left(\frac{\pi}{6}\right)\right) $$ d. $$ \quad 2\left(\cos \left(\frac{\pi}{6}\right)+i \sin \left(\frac{\pi}{6}\right)\right) $$

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We are given $$ z = \sqrt{3} + i $$.

1. Compute the modulus $$ r $$:
   $$
   r = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3 + 1} = \sqrt{4} = 2.
   $$

2. Compute the argument $$ \theta $$:
   $$
   \theta = \arctan{\left(\frac{1}{\sqrt{3}}\right)} = \frac{\pi}{6}.
   $$

3. Write the polar representation:
   $$
   z = 2\left(\cos\left(\frac{\pi}{6}\right) + i \sin\left(\frac{\pi}{6}\right)\right).
   $$

The correct answer is:
d. $$ \quad 2\left(\cos \left(\frac{\pi}{6}\right)+i \sin \left(\frac{\pi}{6}\right)\right) $$.
The polar representation of $$ z = \sqrt{3} + i $$ is $$ 2\left(\cos \left(\frac{\pi}{6}\right) + i \sin \left(\frac{\pi}{6}\right)\right) $$.

The complex number is given by , what is
the polar representation of ?
Select one:
a.
b.
c.
d.

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