The polar form of the complex number -9√3 + 9i is 18(cos(150°) + isin(150°)), which corresponds to option B.
The polar form of a complex number -9√3 + 9i can be found by converting the rectangular coordinates (-9√3, 9) to polar coordinates.
To do this, you calculate the magnitude (r) and the angle (θ) of the position vector of the complex number.
The magnitude is given by r = √(a^2 + b^2), where a is the real part and b is the imaginary part.
Here, r = √((-9√3)^2 + 9^2) = √(243 + 81) = √324 = 18.
To find the angle, you take the arctangent of the imaginary part over the real part, θ = atan(b/a). In this case, θ = atan(9 / -9√3) which simplifies to θ = atan(-1/√3).
This gives us an angle of 150°. Therefore, the polar form is 18(cos(150°) + isin(150°)), which corresponds to option B.
The probable question may be:
What is the polar form of -9√/3+91?
A. 18(cos(120°) + isin(120°))
B. 18(cos(150°) + isin(150°))
C. 324(cos(120°) + isin(120°))
D. 324(cos(150°) + isin(150°))