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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1
If x=cos⁡θ+isin⁡θx=\cos \theta+i \sin \theta and y=cos⁡ϕ+isin⁡ϕy=\cos \phi+i \sin \phi, then xmyn+1xmyn=x^m y^n+\frac{1}{x^m y^n}=
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Correct option: C
2cos⁡(mθ+nϕ)2 \cos (m \theta+n \phi)
Option C (2cos⁡(mθ+nϕ)\cos(m\theta + n\phi)) is correct because by using Euler's formula and simplifying the expression, we arrive at 2cos⁡(mθ+nϕ)\cos(m\theta + n\phi).

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