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Convert each of the complex numbers in the polar form: (7) sqrt 3 + i

Convert each of the complex numbers in the polar form: 

Q : 7    \sqrt{3}+i

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Given problem is
z=\sqrt3+i
Now, let 
r\cos \theta = \sqrt3 \ \ \ and \ \ \ r\sin \theta = 1
Square and add both the sides 
r^2(\cos^2\theta +\sin^2\theta)= (\sqrt3)^2+(1)^2                                                     (\because \cos^2\theta +\sin^2\theta = 1)
r^2= 3+1
r^2 =4
r= 2                                                                                                                         (\because r > 0)
Therefore, the modulus is 2
Now, 
2\cos \theta =\sqrt3 \ \ \ and \ \ \ 2\sin \theta = 1
\cos \theta = \frac{\sqrt3}{2}\ \ \ and \ \ \ \sin \theta =\frac{1}{2}
Since values of Both \cos \theta  and \sin \theta is Positive  and  we know that this is the case in  I quadrant
Therefore,
\theta =\frac{\pi}{6}\ \ \ \ \ \ \ \ \ \ \ \ (lies \ in \ I \ quadrant)
Therefore,
\sqrt3+i= r\cos \theta +ir\sin \theta
               = 2\cos \left (\frac{\pi}{6} \right ) +i2\sin \left (\frac{\pi}{6} \right )
               = 2\left ( \cos \frac{\pi}{6} +i\sin\frac{\pi}{6} \right )

Therefore, the required polar form is   2\left ( \cos \frac{\pi}{6} +i\sin\frac{\pi}{6} \right )

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