If $(\cos {\rm{\theta }} + i\sin {\rm{\theta }}){\rm{\;}}(\cos 2{\rm{\theta }} + i\sin 2{\rm{\theta }}) \ldots \;(\cos n{\rm{\theta }} + i\sin n{\rm{\theta }}) = 1$, then the value of $\theta $ is

$\frac{{2m\pi }}{{n\left( {n + 1} \right)}}$

$\frac{{m\pi }}{{n\left( {n + 1} \right)}}$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

(\cos \mathrm{\theta } + i\sin \mathrm{\theta })\mathrm{\;}(\cos 2\mathrm{\theta } + i\sin 2\mathrm{\theta }) \ldots \;(\cos n\mathrm{\theta } + i\sin n\mathrm{\theta }) = 1

, then the value of

\theta

View answer and explanation

Correct option: C

\frac{{4m\pi }}{{n\left( {n + 1} \right)}}

Option C

\frac{{4m\pi }}{{n\left( {n + 1} \right)}}

is correct because it is derived by using De Moivre's theorem and equating the imaginary part to zero to find the general solution for

\theta