What is the value of
`[-1+isqrt3)//2]^(10)+[-1-isqrt3)//2]^(10)`

Options

A. 1
B. `-1`
C. 2
D. 0

Answer

B

Explanation

We know that `(-1+isqrt3)/(2)omega,`
so, `(-1-isqrt3)/(2)=omega^(2)`
`therefore[(-1+isqrt3)/(2)]^(10)+[(-1-isqrt3)/(2)]^(10)`
`=omega^(10)+omega^(20)=omega^(3xx3+1)+omega^(3xx6+2)`
`=omega^(3)omega^(3)omega+omega^(3)omega^(6)omega^(2)=omega+omega^(2)" "(since omega^(3)=1)`
and `omega+omega^(2)=-1" "(1+omega+omega^(2)=0)`