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

DE MOIVER’S Theorem

 

« Click Here for Previous Topic Click Here for Next Topic »

Click Here for Class XI Classes Maths All Topics Notes

You wish to report grammatical or factual errors within our online articles, you can let us know using the article feedback form.

comments