kingdukkwashere
Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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))

Sagot :

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 θ such that

tan(θ) = (-9√3) / (-9) = √3

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

θ = arctan(√3) - π = π/3 - π = -2π/3

Then the polar form is

18 (cos(-2π/3) + i sin(-2π/3))

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

18 (cos(4π/3) + i sin(4π/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

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.