How do you write the following in trigonometric form and perform the operation given $\frac{1 + \sqrt{3} i}{6 - 3 i}$ $(1+sqrt3i)/(6-3i)$ ?

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How do you write the following in trigonometric form and perform the operation given $\frac{1 + \sqrt{3} i}{6 - 3 i}$ $(1+sqrt3i)/(6-3i)$ ?

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Answer 1 · 2018-07-17T07:29:32

$\Rightarrow 0.0178 + 0.2976 i$ $color(green)(=> 0.0178 + 0.2976 i)$

Explanation:

$\frac{z_{1}}{z_{2}} = (\frac{r_{1}}{r_{2}}) (cos (θ_{1} - θ_{2}) + i sin (θ_{1} - θ_{2}))$ $z_1 / z_2 = (r_1 / r_2) (cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))$

$z_{1} = 1 + 3 i, z_{2} = 6 - 3 i$ $z_1 = 1 + 3 i, z_2 = 6 - 3 i$

$r_{1} = \sqrt{1^{2} + {\sqrt{3}}^{2}} = 2$ $r_1 = sqrt(1^2 + sqrt3^2) = 2$

$θ_{1} = \frac{{tan}^{\sqrt{3}}}{1} = 60^{\circ}^\circ, I Quadrant$ $theta_1 = tan ^ (sqrt3)/ (1) = 60^@ ^@, " I Quadrant"$

$r_{2} = \sqrt{6^{2} + {(- 3)}^{2}} = \sqrt{45}$ $r_2 = sqrt(6^2 + (-3)^2) = sqrt 45$

$θ_{2} = {tan}^{- 1} (- \frac{3}{6}) \approx {333.43}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-3/ 6) ~~ 333.43^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \frac{2}{\sqrt{45}} (cos (60 - 333.43) + i sin (60 - 333.43))$ $z_1 / z_2 = 2/sqrt(45) (cos (60- 333.43) + i sin (60- 333.43))$

$\Rightarrow 0.0178 + 0.2976 i$ $color(green)(=> 0.0178 + 0.2976 i)$

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How do you write the following in trigonometric form and perform the operation given $\frac{1 + \sqrt{3} i}{6 - 3 i}$ $(1+sqrt3i)/(6-3i)$ ?

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Explanation:

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How do you write the following in trigonometric form and perform the operation given $\frac{1 + \sqrt{3} i}{6 - 3 i}$ $(1+sqrt3i)/(6-3i)$ ?