How do you multiply $(1 - i) (- 4 - 3 i)$ $(1-i)(-4-3i)$ in trigonometric form?

Question

1709 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-08T02:29:50

$(1 - i) \cdot (- 4 - 3 i) \approx - 0.28 + i 0.04$ $color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04$

To divide $(1 - i) \cdot (- 4 - 3 i)$ $(1 - i)* (-4 - 3 i)$ using trigonometric form.

$z_{1} = (1 - i), z_{2} = (- 4 - 3 i)$ $z_1 = (1 - i), z_2 = (-4 - 3 i)$

#r_1 = sqrt(-1^2 + 1^2) = sqrt 2

$r_{2} = \sqrt{- 3^{2} + - 4^{2}} = 5$ $r_2 = sqrt(-3^2 + -4^2) = 5$

$θ_{1} = arctan (- \frac{1}{1}) = 315^{\circ}, IV quadrant$ $theta_1 = arctan (-1/1) = 315^@, " IV quadrant"$

$Theta_2 = arctan(-3/-4) = 216.87^@, " III quadrant"$

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

$z_1 / z_2 = sqrt2 / 5 * (cos (315 + 216.87 ) + i sin (315 + 216.87 ))$

$z_1 / z_2 = sqrt2 / 5 * (cos (531.87) + i sin (531.87))$

$color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04$

How do you multiply (1-i)(-4-3i) (1−i)(−4−3i) (1-i)(-4-3i) in trigonometric form?