Question

Let a and b be complex cube roots of unity. If x=7a+2b and y=2a+7b, then evaluate xy.

Answer 1

Answer:

xy = 14a² + 53ab + 14

Step-by-step explanation:

x=7a+2b

y=2a+7b

xy = (7a+2b) (2a+7b)

= 7a (2a+7b) + 2b (2a+7b)

= {(7a X 2a) + (7a X 7b)} + {(2b X 2a) + (2b X 7b)}

= 14a² + 49ab + 4ab + 14b²

= 14a² + 53ab + 14b²