If n is any integer, then (cos Θ + i sin Θ)^{n} = cos nΘ + i sin nΘ. This is known as De Movre’s Theorem.

**Remarks:**

- Writing the binomial expansion of (cos Θ + i sin Θ)
^{n}and equating the real part to cos nΘ and the imaginary part to sin nΘ, we get

cos nΘ = cos^{n} Θ – ^{n}c_{2} cos^{n–2}Θ sin^{2}Θ + ^{n}c_{4} cos^{n–4}Θ sin^{4}Θ + ………

sin nΘ = ^{n}c_{1} cos^{n–1}Θ sinΘ – ^{n}c_{3} cos^{n–3}Θ sin^{3}Θ + ^{n}c_{5} cos^{n–5}Θ sin^{5}Θ +

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