if `omega` is a complex fifth roots of unity and `(1+omega+omega^(2)+omega^(3))^(2005)=A+Bomega+Comega^(2)+Domega^(3)` (Where A,B,C,D are real), the `A^(2)+B^(3)+C^(4)+D^(5)=`

Options

A. 2
B. 1
C. 3
D. None of these

Answer

B

Explanation

`because omega` is a complex fifth roots of unity.
`therefore1+omega+omega^(2)+omega^(3)+omega^(4)=0`
`implies(-omega^(4))^(2005)=A+Bomega+Comega^(2)+Domega^(3)`
`implies-omega^(8020)=A+Bomega+Comega^(2)+Domega^(3)`
`implies-(omega^(5))^(1604)=A+Bomega+Comega^(2)+Domega^(3)`
`implies-1=A+Bomega+Comega^(2)+Domega^(3)`
`impliesA=-1,B=0,C=0,D=0`