CBSE Class 11 Maths Notes: DE MOIVER’S Theorem

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 = cosⁿ Θ – ⁿc₂ cos^n–2Θ sin²Θ + ⁿc₄ cos^n–4Θ sin⁴Θ + ………
sin nΘ = ⁿc₁ cos^n–1Θ sinΘ – ⁿc₃ cos^n–3Θ sin³Θ + ⁿc₅ cos^n–5Θ sin⁵Θ +

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