kingdukkwashere
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What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot ?

9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Note: it is NOT 18(cos(pi/3)+isin(pi/3))

Respuesta :

LammettHash

I think you mean the complex number

-9 - 9√3 i

This number has modulus

|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18

and argument ΞΈ such that

tan(θ) = (-9√3) / (-9) = √3

Since -9 - 9√3 i falls in the third quadrant of the complex plane, we expect ΞΈ to be between -Ο€ and -Ο€/2 radians, so that

ΞΈ = arctan(√3) - Ο€ = Ο€/3 - Ο€ = -2Ο€/3

Then the polar form is

18 (cos(-2Ο€/3) + i sin(-2Ο€/3))

and -2Ο€/3 is the same angle as 2Ο€ - 2Ο€/3 = 4Ο€/3, so the correct choice is

18 (cos(4Ο€/3) + i sin(4Ο€/3))

Answer:

D.18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Step-by-step explanation:

Got it right on Edge 2022

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