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Math Help - Polar Form and De Moivre's Theorem

  1. #1
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    Polar Form and De Moivre's Theorem

    Write each formula in polar form..

    a) 3-3i
    For this, I got sqrt(18)*(cos pi/4 + i sin pi/4)

    b) 1-sqrt(3)i
    For this, I got 2*(cos 5/3 pi + i sin 5/3 pi)

    Use De Moivre's Theorem for:
    1-sqrt (3)i

    I got 32 (cos 25/3 pi + i sin 25/3 pi) = 32i

    Are these correct?
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  2. #2
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    Quote Originally Posted by Jgirl689 View Post
    Write each formula in polar form..

    a) 3-3i
    For this, I got sqrt(18)*(cos pi/4 + i sin pi/4)

    Modulus is correct. Magnitude of angle is correct. Sign on angle is wrong. It's -pi/4 (3-3i lies in the fourth quadrant in the complex plane)

    b) 1-sqrt(3)i
    For this, I got 2*(cos 5/3 pi + i sin 5/3 pi)

    Yep this is correct.

    Use De Moivre's Theorem for:
    (1-sqrt (3)i)^5

    Judging by your answer put the power in for you.

    Your expression is correct, but the final answer is wrong. You'll find that 25pi/3 is equivalent to pi/3

    I got 32 (cos 25/3 pi + i sin 25/3 pi) = 32i

    Are these correct?
    .
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