How do you multiply $(9-2i)(2+i)$ in trigonometric form?

Question

1634 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-25T05:13:43

$color(crimson)((9 - 2 i)* (2 + i) = 18.44 * (0.9701 + i 0.2426)$

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

$z_1 = (9 - 2 i), z_2 = (2 + i)$

$r_1 = sqrt (9^2 + -23^2) = sqrt (85)$

$theta _1 = tan ^-1 (-2/9) = 347.47^@, " IV quadrant"$

$r_2 = sqrt (2^2 + 1^2) = sqrt (5)$

$theta _2 = tan ^-1 (1/2) = 26.57^@ , " I quadrant"$

$z_1 * z_2 = (sqrt 85 * sqrt 5) * (cos(347.47 + 26.57) + i (347.47 + 26.57))$

$color(crimson)((9 - 2 i)* (2 + i) = 18.44 * (0.9701 + i 0.2426)$

How do you multiply (9-2i)(2+i) (9-2i)(2+i) in trigonometric form?