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22 September, 22:14

Find (-1 - i sqrt (3)) ^10. Express in rectangular form.

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  1. 23 September, 01:11
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    Z = - 1 - i√3

    x = - 1, y = - √3

    r = |z| = √ (-1) ² + (-√3) ² = √ (1 + 3) = √4 = 2

    Ф = arc tan (-√3/-1) = arc tan (√3) = 60° = π/3

    r ^n (cos nФ + i sinФ) = 2^10 (cos (10π/3) + i sin (10π/3)) =

    = 2^10 (-1/2 - i √3/2) = 2^9 ( - 1 - i √3)
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