JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

\alpha ,\beta

and

\gamma

are angles such that

\tan \alpha + \tan \beta + \tan \gamma = \tan \alpha \tan \beta \tan \gamma

and

x = \cos \alpha + i\sin \alpha ,\;\;y = \cos \beta + i\sin \beta

and

z = \cos \gamma + i\sin \gamma

, then

xyz

is equal to

View answer and explanation

Correct option: C

+ 1\,\mathrm{or}\, - 1

Option C (

+ 1\;\mathrm{or}\; - 1

) is correct because by using the given condition and trigonometric identities, we can show that

xyz

can be either +1 or -1.

More Questions from COMPLEX NUMBERS

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

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\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}