If `alpha` is a cube root of unity, then find the value of `|[alpha,alpha^3,alpha^5],[alpha^3,alpha^5,alpha],[alpha^5,alpha,alpha^3]|`

If alpha is a cube of unity , then the value of |{:(alpha,alpha^(3),alpha^(5)),(alpha^(3),alpha^(5),alpha),(alpha^(5),alpha,alpha^(3)):}| is equal to

If alpha is a non-real fifth root of unity, then the value of 3^(|1+alpha+alpha^(2),alpha^(-2)-alpha^(-1)| , is

If alpha is a non-real fifth root of unity, then the value of 3^(|1+alpha+alpha^(2),alpha^(-2)-alpha^(-1)| , is

If alpha=cos ((2pi)/5)+isin((2pi)/5) , then find the value of alpha+alpha^2+alpha^3+alpha^4

If alpha is an imaginary cube root of unity,then for n in N , the value of (alpha)^(3n+1)+(alpha)^(3n+3)+(alpha)^(3n+5) is

If alpha is an imaginary fifth root of unity, then log_(2)|1+alpha+alpha^(2)+alpha^(3)-1/alpha|=

If alpha Is the fifth root of unity, then, prove that : Log_2|1+alpha+alpha^(2)+alpha^(3)-(1/alpha)|=1

If alpha is an imaginary fifth root of unity, then log_(2)|1+alpha+alpha^(2)+alpha^(3)-1/alpha|=

If alpha=cos((2 pi)/(5))+i sin((2 pi)/(5)), then find the value of alpha+alpha^(2)+alpha^(3)+alpha^(4)

If alpha is a root of x^(3)-x-1=0, compute the value of alpha^(10)+2 alpha^(8)-alpha^(7)-3 alpha^(6)-3 alpha^(5)+4 alpha^(4)+2 alpha^(3)-4 alpha^(2)-6 alpha