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

Question

Yoselin Chang

Mathematics

2 July, 17:32

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

+4

Answers (1)

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Leslie Frank · Answer 1

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)