How do you divide $\frac{i - 1}{- i + 10}$ $( i-1) / (-i +10 )$ in trigonometric form?

Question

How do you divide $\frac{i - 1}{- i + 10}$ $( i-1) / (-i +10 )$ in trigonometric form?

1 Answer

Impact of this question

1833 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-28T11:50:03

$\Rightarrow - 0.1089 + 0.0891 i, II Quadrant$ $color(indigo)(=> -0.1089 + 0.0891 i, " II Quadrant"$

Explanation:

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

$z_{1} = - 1 + i, z_{2} = 10 - i$ $z_1 = -1 + i, z_2 = 10 - i$

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

$θ_{1} = {tan}^{- 1} (\frac{1}{- 1}) 135^{\circ}, II Quadrant$ $theta_1 = tan ^-1 (1/ -1) 135^@ , " II Quadrant"$

$r_{2} = \sqrt{10^{2} + {(- 1)}^{2}} = \sqrt{101}$ $r_2 = sqrt(10^2 + (-1)^2) = sqrt 101$

$θ_{2} = {tan}^{- 1} (- \frac{1}{10}) \approx {354.29}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-1/ 10) ~~ 354.29^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{2}{101}} (cos (135 - 354.29) + i sin (135 - 354.29))$ $z_1 / z_2 = sqrt(2 / 101) (cos (135 - 354.29) + i sin (135 - 354.29))$

$\Rightarrow - 0.1089 + 0.0891 i, II Quadrant$ $color(indigo)(=> -0.1089 + 0.0891 i, " II Quadrant"$

Science

Math

Humanities

... and beyond

How do you divide $\frac{i - 1}{- i + 10}$ $( i-1) / (-i +10 )$ in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide ( i-1) / (-i +10 )i−1−i+10( i-1) / (-i +10 ) in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{i - 1}{- i + 10}$ $( i-1) / (-i +10 )$ in trigonometric form?