What is the polar form of Negative 9 StartRoot 3 EndRoot + 9 i?

Step-by-step explanation:

In the rectangular complex number -9√3 + 9i, which has a standard form a + bi, the a = -9√3 and the b = 9. We need this in polar form (r, θ) where

and filling in:

(notice we do not put the i in there with the 9).

so

r = 18. Now let's move on to the angle, which is a little more difficult. The angle is found in the inverse tangent ratio:

so filling that in, we have:

Since tangent is the side opposite over the side adjacent, y is positive and x is negative in the second quadrant. This is a 30 degree angle in QII, which has a reference angle of 150 degrees. This angle in radians is , so the polar form of that number is (18, )

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