JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

n

is a positive integer, then

{\left( {1 + i\sqrt 3 } \right)^n} + {\left( {1 - i\sqrt 3 } \right)^n}

is equal to

View answer and explanation

Correct option: C

{2^{n + 1}}\cos \frac{{n\pi }}{3}

Option C (

{2^{n + 1}}\cos \frac{{n\pi }}{3}

) is correct because by converting the complex numbers to polar form and applying De Moivre's theorem, the expression simplifies to

{2^{n + 1}}\cos \frac{{n\pi }}{3}

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}