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saul85 [17]
3 years ago
8

use demoivre's theorem to evaluate the expression (3(cos cos(5pie/6)+isin(5pie/y))))^4 write the answer in rectangular form.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0

By DeMoivre's theorem,

(3 (cos(5<em>π</em>/6) + <em>i</em> sin(5<em>π</em>/6)))⁴ = 3⁴ (cos(4×5<em>π</em>/6) + <em>i</em> sin(4×5<em>π</em>/6))

… = 81 (cos(20<em>π</em>/6) + <em>i</em> sin(20<em>π</em>/6))

… = 81 (cos(10<em>π</em>/3) + <em>i</em> sin(10<em>π</em>/3))

… = 81 (cos(-2<em>π</em>/3) + <em>i</em> sin(-2<em>π</em>/3))

… = 81 (cos(2<em>π</em>/3) - <em>i</em> sin(2<em>π</em>/3))

… = 81 (-1/2 + √3/2 <em>i </em>)

… = -81/2 + 81√3/2 <em>i</em>

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