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

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

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Answer 1 · 2018-06-25T05:07:47

$(10 - 2 i) \cdot (3 - i) = 18.44 \cdot (- 0.9762 - i 0.217)$ $color(green)((10 - 2 i)* (3 - i) = 18.44 * (-0.9762 - i 0.217)$

Explanation:

$z_{1} \cdot z_{2} = (r_{1} \cdot r_{2}) \cdot (({cos θ}_{1} + θ_{2}) + i sin (θ_{1} + θ_{2}))$ $z_1 * z_2 = (r_1 * r_2) * ((cos theta_1 + theta_2) + i sin (theta_1 + theta_2))$

$z_{1} = (- 5 - 3 i), z_{2} = (3 - i)$ $z_1 = (-5 - 3 i), z_2 = (3 - i)$

$r_{1} = \sqrt{- 5^{2} + - 3^{2}} = \sqrt{34}$ $r_1 = sqrt (-5^2 + -3^2) = sqrt (34)$

$θ_{1} = {tan}^{- 1} (- \frac{3}{- 5}) = {210.96}^{\circ}, III quadrant$ $theta _1 = tan ^-1 (-3/-5) = 210.96^@, " III quadrant"$

$r_{2} = \sqrt{3^{2} + - 1^{2}} = \sqrt{10}$ $r_2 = sqrt (3^2 + -1^2) = sqrt (10)$

$θ_{2} = {tan}^{- 1} (- \frac{1}{3}) = - {18.43}^{\circ} = {341.57}^{\circ}, IV quadrant$ $theta _2 = tan ^-1 (-1/3) = -18.43^@ = 341.57^@, " IV quadrant"$

$z_{1} \cdot z_{2} = (\sqrt{34} \cdot \sqrt{10}) \cdot (cos (210.96 + 341.57) + i (210.96 + 341.57))$ $z_1 * z_2 = (sqrt34 * sqrt 10) * (cos(210.96 + 341.57) + i (210.96 + 341.57))$

$(10 - 2 i) \cdot (3 - i) = 18.44 \cdot (- 0.9762 - i 0.217)$ $color(green)((10 - 2 i)* (3 - i) = 18.44 * (-0.9762 - i 0.217)$

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

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