Question

The value of $(-1+\sqrt{-3}{)}^{62}+(-1-\sqrt{-3}{)}^{62}$ is

• A. $2^{62}$
• B. $2^{-62}$
• C. $-2^{62}$
• D. $0$

Answer 1

The correct option is C $-2^{62}$

Now, $w=\frac{-1+\sqrt{-3}}{2}$

$2w=-1+\sqrt{-3}$

$(-1++\sqrt{-3}{)}^{62}=2^{62}.w^{62}$

$=2^{62}{w}^2$

Also,

$w^2=\frac{-1-\sqrt{-3}}{2}$

$2w^2=(-1-\sqrt{-3})$

$(-1-\sqrt{-3}{)}^{62}=2^{62}{w}^{124}$

$=2^{62}w$

Also, $w+w^2=-1$

So, Sum $=2^{62}(w+w^2)=-2^{62}$

(c)