Question

Let omega be a complex number such that omega^3 = 1. Find all possible values of {1}{1 + \omega} + {1}{1 + \omega^2}. Enter all the possible values, separated by commas.

Answer 1

1 is Answer.

Explanation

`(1)/(1+omega^(2) ) + (1)/(1+omega )\\`

=
`((-1)*(omega + 1))/(omega^(2)  )`

As we know that ω²+ω+1=0

Thus putting in above equation, we get

=
`(1)/((-1)*omega ) + (1)/((-1)*omega^(2)  )`

Rearranging and simplifying:

=
`(-1)/(omega ) + (-1)/(omega^(2)  )`

=
`((-1)*(omega + 1))/(omega^(2)  )`

=
`((-1)*(- omega^(2) ))/(omega^(2)  )`

= 1 Answer