( 3+ i 2 )^6+ ( i -3 2 )^6 is equal to

MCQ

$\left(\frac{\sqrt{3}+ i }{2}\right)^6+\left(\frac{ i -\sqrt{3}}{2}\right)^6$ is equal to

✓
$-2$
B
$0$
C
2
D
1

✓

Answer

Correct option: A.

$-2$

(A)
$\left(\frac{\sqrt{3}+ i }{2}\right)^6+\left(\frac{ i -\sqrt{3}}{2}\right)^6$
$=\left(\frac{-1+\sqrt{3} i }{2 i }\right)^6+\left(\frac{-1-\sqrt{3} i }{2 i }\right)^6$
$=\frac{1}{i^6}\left[(\omega)^6+\left(\omega^2\right)^6\right]$
$\ldots\left[\because \omega=\frac{-1+\sqrt{3} i }{2}, \omega^2=\frac{-1-\sqrt{3} i }{2}\right]$
$=-\left[\left(\omega^3\right)^2+\left(\omega^3\right)^4\right]=-(1+1)=-2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The probability that a student knows the correct answer to a multiple-choice question is

$\frac{2}{3}$. If the student does not know the answer, then the student guesses the answer. Theprobability of the guessed answer being correct is $\frac{1}{4}$. Given that the student has answered

the question correctly, the probability that the student knows the correct answer is

→

If odds against solving a question by three students are $2: 1,5: 2$ and $5: 3$ respectively, then probability that the question is solved only by one student is

→

If the number of elements in the sets G and A are 3 and 4 respectively, then match the items of List I with those of List II.

	List I		List II
(a)	The number of non bijective functions from GG to G	I.	24
(b)	The number of bijective functions from A to A	II.	0
(c)	The number of functions from G to GA	III.	1728
(d)	The number of surjective functions from A to AA	IV.	12
		V.	19683