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

Answer:

1 is Answer.

Step-by-step explanation

$\frac{1}{1+omega^{2} } + \frac{1}{1+omega }$

= $\frac{(-1)*(omega + 1)}{omega^{2} }$

As we know that ω²+ω+1=0

Thus putting in above equation, we get

= $\frac{1}{(-1)*omega } + \frac{1}{(-1)*omega^{2} }$

Rearranging and simplifying:

= $\frac{-1}{omega } + \frac{-1}{omega^{2} }$

= $\frac{(-1)*(omega + 1)}{omega^{2} }$

= $\frac{(-1)*(- omega^{2} )}{omega^{2} }$

= 1 Answer