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Simplify a quotient of powers of cos + i sin by De Moivre's theorem

This type of question, asked 2 times: 20 Apr 2025 S2, 17 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    140
    The value of (cos⁡θ+isinθ)4(sin⁡θ+icosθ)5=\frac{(\cos\theta+isin\theta)^{4}}{(\sin\theta+icos\theta)^{5}}=where i=−1i =\sqrt{- 1}

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  2. Question 2

    17 Apr 2026 S2

    52
    (cos⁡2θ+isin⁡2θ)7(cos⁡4θ+isin⁡4θ)3=\dfrac{(\cos 2\theta + i\sin 2\theta)^7}{(\cos 4\theta + i\sin 4\theta)^3} =

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