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

Question

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

in progress 0
Ngọc Khuê 3 weeks 2021-08-31T12:25:21+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-31T12:27:11+00:00

    Answer:

    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

    r=\sqrt{a^2+b^2} and filling in:

    r=\sqrt{(-9\sqrt{3})^2+(9)^2 } (notice we do not put the i in there with the 9).

    r=\sqrt{243+81} 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:

    tan^{-1}(\frac{b}{a}) so filling that in, we have:

    tan^{-1}(\frac{9}{-9\sqrt{3} })=\frac{1}{-\sqrt{3} } 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 \frac{5\pi}6}, so the polar form of that number is (18, \frac{5\pi}{6})

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )