How do you divide $\frac{7 + 5 i}{1 - 3 i}$ $(7+5i)/(1-3i)$ in trigonometric form?

Question

How do you divide $\frac{7 + 5 i}{1 - 3 i}$ $(7+5i)/(1-3i)$ in trigonometric form?

1 Answer

Impact of this question

1656 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-26T14:53:08

$\Rightarrow - 0.8 + 2.6 i,$ $color(maroon)(=> -0.8 + 2.6 i),$ II QUADRANT

Explanation:

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

$z_{1} = 7 + 5 i, z_{2} = 1 - 3 i$ $z_1 = 7 + 5 i, z_2 = 1 - 3 i$

$r_{1} = {\sqrt{7^{2} + 5^{2}}}^{2}) = \sqrt{74}$ $r_1 = sqrt(7^2 + 5^2)^2) = sqrt 74$

$θ_{1} = {tan}^{- 1} (\frac{5}{7}) = {35.5377}^{\circ} =, I Quadrant$ $theta_1 = tan ^ -1 (5 / 7) = 35.5377^@ = , " I Quadrant"$

$r_{2} = \sqrt{1^{2} + {(- 3)}^{2}} = \sqrt{10}$ $r_2 = sqrt(1^2 + (-3)^2) = sqrt 10$

$θ_{2} = {tan}^{- 1} (- \frac{3}{1}) \approx {288.4349}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-3/ 1) ~~ 288.4349^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{74}{10}} (cos (35.5377 - 288.4349) + i sin (35.5377 - 288.4349))$ $z_1 / z_2 = sqrt(74 / 10) (cos (35.5377 - 288.4349) + i sin (35.5377 - 288.4349))$

$\Rightarrow - 0.8 + 2.6 i,$ $color(maroon)(=> -0.8 + 2.6 i),$ II QUADRANT

Science

Math

Humanities

... and beyond

How do you divide $\frac{7 + 5 i}{1 - 3 i}$ $(7+5i)/(1-3i)$ in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide 7+5i1−3i (7+5i)/(1-3i) in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{7 + 5 i}{1 - 3 i}$ $(7+5i)/(1-3i)$ in trigonometric form?