JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

The value of

\frac{(\cos 2 \theta-i \sin 2 \theta)^7(\cos 3 \theta+i \sin 3 \theta)^{-5}}{(\cos 4 \theta+i \sin 4 \theta)^{12}(\cos 5 \theta+i \sin 5 \theta)^{-6}}

View answer and explanation

Correct option: D

\cos 47 \theta-i \sin 47 \theta

Option D (

\cos 47 \theta - i \sin 47 \theta

) is correct because after applying De Moivre's theorem and simplifying, the expression equals

\cos 47 \theta - i \sin 47 \theta

More Questions from COMPLEX NUMBERS

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

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\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}