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ivanzaharov [21]
3 years ago
12

Use de moivre's theorem to write [2(cos 12 degrees + i sin 12 degrees)]^5 in standard form

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

DeMoivre's theorem says

(2 (cos(12°) + <em>i</em> sin(12°)))⁵ = 2⁵ (cos(5×12°) + <em>i</em> sin(5×12°))

… = 32 (cos(60°) + <em>i</em> sin(60°))

… = 32 (1/2 + √3/2 <em>i</em> )

… = 16 + 16√3 <em>i</em>

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