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Find the value of ((cosθ+isinθ)⁴)/((cosθ-isinθ)³).

1. cos 5θ+isin 5θ
2. cos 7θ+isin 7θ
3. cos 4θ+isin 4θ
4. cos θ+isin θ

Correct answer: cos 7θ+isin 7θ

Solution

(cosT+isinT)^4 = e^(i4T) and (cosT-isinT)^3 = e^(-i3T), so the ratio is e^(i4T)/e^(-i3T) = e^(i7T) = cos7T + isin7T.

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