If and are the roots of x^2+x+1=0 , then what is _ j=0 ^3 ( ^j+ ^j ) equal to?

Step-by-step solution

x^2+x+1=0 = and = ^2 _ j=0 ^3 ( ^j+ ^j )= ( ^0+ ^1+ ^2+ ^3 )+ ( ^0+ ^1+ ^2+ ^3 ) sum of 3 consecutive powers of and =0 _ j=0 ^3 ( ^j+ ^j )= ^0+ ^0=2