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5 December, 01:27

Use DeMoivre's Theorem to find (3cis (pi/6)) ^3.

a.) (27sqrt3) / 2 + 27/2 i

b.) (9sqrt3) / 2 + 9/2 i

c.) 27i

d.) 9i

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Answers (1)
  1. 5 December, 01:43
    0
    C. 27i

    Step-by-step explanation:

    Given the complex number in polar coordinate expressed as

    z = r (cos∅+isin∅)

    zⁿ = {r (cos∅+isin∅) }ⁿ

    According to DeMoivre's Theorem;

    zⁿ = rⁿ (cosn∅+isinn∅)

    Given the complex number;

    (3cis (pi/6)) ^3

    = {3 (cosπ/6 + isinπ/6) }^3

    Using DeMoivre's Theorem;

    = 3³ (cos3π/6 + isin3π/6)

    = 3³ (cosπ/2 + isinπ/2)

    = 3³ (0 + i (1))

    = 27i

    The right answer is 27i
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