Represent √3+i in polar form?

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Answer 1 · 2017-10-21T12:19:27

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Tony B

Answer 2 · 2017-10-21T12:21:37

$\sqrt{3} + i = 2 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))$ $sqrt(3) + i = 2(cos(pi/6) + isin(pi/6))$

Let $\sqrt{3} + i = z$ $sqrt(3) + i = z$

Modulus of $z$ $z$ :

$| z | = \sqrt{{\sqrt{3}}^{2} + 1^{2}} = \sqrt{4} = 2 = r$ $|z| = sqrt(sqrt(3)^2 + 1^2) = sqrt(4) = 2 = r$

Argument of $z$ $z$ :

$arctan (\frac{1}{\sqrt{3}}) = \frac{π}{6} = θ$ $arctan(1/sqrt(3)) = pi/6 = theta$

$z = r (cos (θ) + i sin (θ)) = 2 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))$ $z = r(cos(theta) + isin(theta)) = 2(cos(pi/6) + isin(pi/6))$