How do you divide $\frac{- i + 4}{2 i + 7}$ $( -i+4) / (2i +7 )$ in trigonometric form?

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Answer 1 · 2018-06-28T04:16:36

$\frac{4 - i}{7 + 2 i} \approx 0.4905 + i 0.2831$ $color(violet)((4 -i) / (7 + 2i) ~~ 0.4905 + i 0.2831$

To divide $\frac{4 - i}{7 + 2 i}$ $(4 - i) / (7 + 2i)$ using trigonometric form.

$z_{1} = (4 - i), z_{2} = (7 + 2 i)$ $z_1 = (4 - i), z_2 = (7 + 2i)$

#r_1 = sqrt(4^2 + 1^2) = sqrt 17

$r_{2} = \sqrt{7^{2} + - 2^{2}} = \sqrt{53}$ $r_2 = sqrt(7^2 + -2^2) = sqrt53$

$θ_{1} = arctan (- \frac{1}{4}) = {345.96}^{\circ}, IV quadrant$ $theta_1 = arctan (-1/4) = 345.96^@, " IV quadrant"$

$Theta_2 = arctan(2/7) = 15.95^@, " I quadrant"$

$z_1 / z_2 = (r_1 / r_2) * (cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))$

$z_1 / z_2 = sqrt(17/53) * (cos (345.96 - 15.95 ) + i sin (345.96 - 15.95 ))$

$z_1 / z_2 = 0.5664 * (cos (-330.01) + i sin (-330.01))$

$color(violet)((4 -i) / (7 + 2i) ~~ 0.4905 + i 0.2831$

How do you divide ( -i+4) / (2i +7 )−i+42i+7( -i+4) / (2i +7 ) in trigonometric form?