How do you write the following in trigonometric form and perform the operation given $(1+sqrt3i)/(6-3i)$ ?

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Answer 1 · 2018-07-17T07:29:32

$color(green)(=> 0.0178 + 0.2976 i)$

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

$z_1 = 1 + 3 i, z_2 = 6 - 3 i$

$r_1 = sqrt(1^2 + sqrt3^2) = 2$

$theta_1 = tan ^ (sqrt3)/ (1) = 60^@ ^@, " I Quadrant"$

$r_2 = sqrt(6^2 + (-3)^2) = sqrt 45$

$theta_2 = tan ^-1 (-3/ 6) ~~ 333.43^@, " IV Quadrant"$

$z_1 / z_2 = 2/sqrt(45) (cos (60- 333.43) + i sin (60- 333.43))$

$color(green)(=> 0.0178 + 0.2976 i)$

How do you write the following in trigonometric form and perform the operation given (1+sqrt3i)/(6-3i)(1+sqrt3i)/(6-3i)?