Value of ( -1+-3 2 )^ 40 + ( -1--3 2 )^ 40 is - Vidyadip

MCQ

Value of $\left(\frac{-1+\sqrt{-3}}{2}\right)^{40}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{40}$ is

A
$0$
B
1
C
2
✓
$-1$

✓

Answer

Correct option: D.

$-1$

(D)
Using $\left(\frac{-1+ i \sqrt{3}}{2}\right)^{ n }+\left(\frac{-1- i \sqrt{3}}{2}\right)^{ n }=-1$
i.e., $\omega^{ n }+\omega^{2 n }=-1$ if n is $a + ve$ integer other than multiple of 3. , we get
$\left(\frac{-1+\sqrt{-3}}{2}\right)^{40}+\left(\frac{-1-\sqrt{-3}}{2}\right)^{40}=-1$

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