How do you divide $\frac{3 i + 7}{- 7 i + 8}$ $( 3i +7) / (- 7 i + 8 )$ in trigonometric form?

Question

How do you divide $\frac{3 i + 7}{- 7 i + 8}$ $( 3i +7) / (- 7 i + 8 )$ in trigonometric form?

1 Answer

Impact of this question

1432 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-24T05:48:06

$\Rightarrow 0.7164 (- 0.3138 + i 0.9495)$ $color(maroon)(=> 0.7164 ( -0.3138 + i 0.9495)$

Explanation:

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

$z_{1} = 7 + i 3, z_{2} = 8 - i 7$ $z_1 = 7 + i 3, z_2 = 8 - i 7$

$r_{1} = \sqrt{7^{2} + 3^{2}} = \sqrt{58}$ $r_1 = sqrt(7^2 + 3^2) = sqrt 58$

$θ_{1} = {tan}^{- 1} (\frac{7}{3}) = {66.8}^{\circ}$ $theta_1 = tan ^ (-1) (7/3) = 66.8 ^@$

$r_{2} = \sqrt{8^{2} + {(7)}^{2}} = \sqrt{113}$ $r_2 = sqrt(8^2 + (7)^2) = sqrt 113$

$θ_{2} = {tan}^{- 1} (- \frac{7}{8}) = - {41.19}^{\circ} = {318.51}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-7/ 8) = -41.19^@ = 318.51^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{58}{113}} (cos (66.8 - 318.51) + i sin (66.8 - 318.51))$ $z_1 / z_2 = sqrt(58/113) (cos (66.8- 318.51) + i sin (66.8- 318.51))$

$\Rightarrow 0.7164 (- 0.3138 + i 0.9495)$ $color(maroon)(=> 0.7164 ( -0.3138 + i 0.9495)$

Science

Math

Humanities

... and beyond

How do you divide $\frac{3 i + 7}{- 7 i + 8}$ $( 3i +7) / (- 7 i + 8 )$ in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide 3i+7−7i+8( 3i +7) / (- 7 i + 8 ) in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{3 i + 7}{- 7 i + 8}$ $( 3i +7) / (- 7 i + 8 )$ in trigonometric form?