How do you multiply $(3-5i)(1-16i)$ in trigonometric form?

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Answer 1 · 2018-07-08T01:52:59

$color(brown)((-3 - 5 i) * (1 - 16 i) ~~ -0.323 + i 0.1673$

To divide $(-3 - 5 i)* (1 - 16 i)$ using trigonometric form.

$z_1 = (-3 - 5 i), z_2 = (1 - 16 i)$

#r_1 = sqrt(-3^2 + 5^2) = sqrt 34

$r_2 = sqrt(1^2 + -16^2) = sqrt 257$

$theta_1 = arctan (-5/-3) = 239.04^@, " III quadrant"$

$Theta_2 = arctan(-16/1) = 273.58^@, " IV quadrant"$

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

$z_1 / z_2 = sqrt(34/257) * (cos (239.04 + 273.58 ) + i sin (239.04 + 273.58 ))$

$z_1 / z_2 = sqrt(34/257) * (cos (512.62) + i sin (512.62))$

$color(brown)((-3 - 5 i) * (1 - 16 i) ~~ -0.323 + i 0.1673$

How do you multiply (3-5i)(1-16i) (3-5i)(1-16i) in trigonometric form?