The value of $\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}$ is
36 views
0 Votes
0 Votes

The value of $\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}$ is

(A) 0

(B) 1

(C) -1

(D) 2

1 Answer

0 Votes
0 Votes
 
Best answer

SOLUTION —

$\left(\frac{-1+\sqrt{-3}}{2}\right)^{100}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{100}$

$=(\omega)^{100}+\left(\omega^2\right)^{100}$

$=\left(\omega^3\right)^{39} \omega+\left(\omega^3\right)^{66}\omega^2$

$=\omega+\omega^2$$ $$\quad\left(\because \omega^3=1\right)$

$=-1$

So, The correct option will be (C).

RELATED DOUBTS

1 Answer
2 Votes
2 Votes
161 Views
1 Answer
2 Votes
2 Votes
179 Views
1 Answer
0 Votes
0 Votes
54 Views
Peddia is an Online Question and Answer Website, That Helps You To Prepare India's All States Boards & Competitive Exams Like IIT-JEE, NEET, AIIMS, AIPMT, SSC, BANKING, BSEB, UP Board, RBSE, HPBOSE, MPBSE, CBSE & Other General Exams.
If You Have Any Query/Suggestion Regarding This Website or Post, Please Contact Us On : [email protected]

CATEGORIES