trig

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Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.

[2(cos 240° + i sin 240°)]^5

  • trig -

    z = 2(cos 240° + i sin 240°) =

    2 exp(4/3 pi i)

    z^5 = 2^5 exp(20/3 pi i) =

    32 exp(2/3 pi i) =

    -16 + 16 sqrt(3) i

  • trig -

    (2cis240°)^5 = 2^5 cis(5*240°)
    = 32 cis1200°
    = 32 cis120°
    = -16 + 16√3 i

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