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# How do you divide  (-4+5i)/(6+i)  in trigonometric form?

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#### Explanation

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#### Explanation:

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1
Jun 24, 2018

color(purple)(=> 1.05 (-0.482 + i 0.876)

#### Explanation:

z_1 / z_2 = r_1/ r_2 (cos (theta_1 + thet_2) + i sin (theta_1 + theta_2)

${z}_{1} = \left(- 4 + i 5\right) , {z}_{2} = \left(6 + i\right)$

$\implies {r}_{1} = \sqrt{{4}^{2} + {5}^{2}} = \sqrt{41} = 6.4$

${\theta}_{1} = {\tan}^{- 1} \left(\frac{5}{-} 4\right) = - {51.34}^{\circ} = {128.26}^{\circ} , \text{ II Quadrant}$

$\implies {r}_{2} = \sqrt{{1}^{2} + {6}^{2}} = \sqrt{37} = 6.08$

${\theta}_{2} = {\tan}^{- 1} \left(\frac{1}{6}\right) = {9.46}^{\circ}$

z_1 / z_2 = sqrt41/sqrt37 (cos (128.26 - 9.46) + i sin(128.26 - 9.46)0

color(purple)(=> 1.05 (-0.482 + i 0.876)

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