How do you perform the operation in trigonometric form $(0.45 (cos (310) + i sin (310))) (0.6 (cos (200) + i sin (200)))$ $(0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))$ ?

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How do you perform the operation in trigonometric form $(0.45 (cos (310) + i sin (310))) (0.6 (cos (200) + i sin (200)))$ $(0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))$ ?

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Answer 1 · 2017-01-05T08:20:26

$(0.45 ({cos 310}^{\circ} + i {sin 310}^{\circ})) (0.6 ({cos 200}^{\circ} + i {sin 200}^{\circ})) = 0.27 (- \frac{\sqrt{3}}{2} + \frac{1}{2} i)$ $(0.45(cos310^@+isin310^@))(0.6(cos200^@+isin200^@))=0.27(-sqrt3/2+1/2i)$

Explanation:

Two complex numbers in polar form $z_{1} = r_{1} (cos α + i sin α)$ $z_1=r_1(cosalpha+isinalpha)$ and $z_{2} = r_{2} (cos β + i sin β)$ $z_2=r_2(cosbeta+isinbeta)$ can be multiplied as under,

$z_{1} \cdot z_{2} = r_{1} \cdot r_{2} [cos α cos β + i cos α sin β + i sin α cos β + i^{2} sin α sin β]$ $z_1*z_2=r_1*r_2[cosalphacosbeta+icosalphasinbeta+isinalphacosbeta+i^2sinalphasinbeta]$

= $r_{1} \cdot r_{2} [(cos α cos β - sin α sin β) + i (cos α sin β + sin α cos β)]$ $r_1*r_2[(cosalphacosbeta-sinalphasinbeta)+i(cosalphasinbeta+sinalphacosbeta)]$

= $r_{1} \cdot r_{2} [cos (α + β) + i sin (α + β)]$ $r_1*r_2[cos(alpha+beta)+isin(alpha+beta)]$

Hence $(0.45 ({cos 310}^{\circ} + i {sin 310}^{\circ})) (0.6 ({cos 200}^{\circ} + i {sin 200}^{\circ}))$ $(0.45(cos310^@+isin310^@))(0.6(cos200^@+isin200^@))$

= $0.45 \times 0.6 (cos (310^{\circ} + 200^{\circ}) + i sin (310^{\circ} + 200^{\circ}))$ $0.45xx0.6(cos(310^@+200^@)+isin(310^@+200^@))$

= $0.27 ({cos 510}^{\circ} + i {sin 510}^{\circ})$ $0.27(cos510^@+isin510^@)$

= $0.27 (cos (360^{\circ} + 150^{\circ}) + i sin (360^{\circ} + 150^{\circ}))$ $0.27(cos(360^@+150^@)+isin(360^@+150^@))$

= $0.27 ({cos 150}^{\circ} + i {sin 150}^{\circ})$ $0.27(cos150^@+isin150^@)$

= $0.27 (- \frac{\sqrt{3}}{2} + \frac{1}{2} i)$ $0.27(-sqrt3/2+1/2i)$

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How do you perform the operation in trigonometric form $(0.45 (cos (310) + i sin (310))) (0.6 (cos (200) + i sin (200)))$ $(0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))$ ?

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Explanation:

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Science

Math

Humanities

... and beyond

How do you perform the operation in trigonometric form (0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))(0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))?

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Explanation:

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How do you perform the operation in trigonometric form $(0.45 (cos (310) + i sin (310))) (0.6 (cos (200) + i sin (200)))$ $(0.45(cos(310)+isin(310)))(0.6(cos(200)+isin(200)))$ ?