trigonometry

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Use De Moivre’s Theorem to simplify each expression. Write the answer in the form a + bi.


{1 - i(/3)}^4

  • trigonometry -

    I will assume you know the theorem and the common variables used in it

    r = √(1^2 + (1/3)^2 )
    = √(1 + 1/9)
    = √(10/9)
    √10/3

    let the angle be Ø
    cosØ = 1/(√10/3) = 3/√10
    sinØ = (-1/3) / (√10/3) = -3/√10 , so Ø is in IV and Ø = 341.565°

    so (1 - (1/3) i )^4 = (√10/3)^4 [ cos 4(341.565° + i sin 4(341.564°)
    = (100/81) [ .28 + (-.96i) ]
    = 28/81 - 96/81i
    = 28/81 - 32/27 i
    =

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