How do you divide $\frac{7 + 8 i}{2 + i}$ $(7+8i) / (2+i)$ in trigonometric form?

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How do you divide $\frac{7 + 8 i}{2 + i}$ $(7+8i) / (2+i)$ in trigonometric form?

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Answer 1 · 2018-08-01T07:25:26

$\Rightarrow 4.4 + 1.8 i, I Quadrant$ $color(indigo)(=> 4.4 + 1.8 i, " I Quadrant"$

Explanation:

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

$z_{1} = 7 + 8 i, z_{2} = 2 + i$ $z_1 = 7 + 8 i, z_2 = 2 + i$

$r_{1} = {\sqrt{7^{2} + 8^{2}}}^{2}) = \sqrt{113}$ $r_1 = sqrt(7^2 + 8^2)^2) = sqrt 113$

$θ_{1} = {tan}^{- 1} (\frac{8}{7}) = {48.8141}^{\circ}, I Quadrant$ $theta_1 = tan ^-1 (8/ 7) = 48.8141^@ , " I Quadrant"$

$r_{2} = \sqrt{2^{2} + {(1)}^{2}} = \sqrt{5}$ $r_2 = sqrt(2^2 + (1)^2) = sqrt 5$

$θ_{2} = {tan}^{- 1} (\frac{1}{2}) \approx {26.5651}^{\circ}, I Quadrant$ $theta_2 = tan ^-1 (1/ 2) ~~ 26.5651^@, " I Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{113}{5}} (cos (48.8141 - 26.5651) + i sin (48.8141 - 26.5651))$ $z_1 / z_2 = sqrt(113 / 5) (cos (48.8141 - 26.5651) + i sin (48.8141 - 26.5651))$

$\Rightarrow 4.4 + 1.8 i, I Quadrant$ $color(indigo)(=> 4.4 + 1.8 i, " I Quadrant"$

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How do you divide $\frac{7 + 8 i}{2 + i}$ $(7+8i) / (2+i)$ in trigonometric form?

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