Hello,
I am studying for examinations and encountered a problem I do not know how to solve:
Let w (omega) be a solution of the equation x^2 + x + 1 = 0
Then w^10 + w^5 + 3 = ?
I first replaced x with w (omega)
which yields
w^2 + w + 1 = 0
What I actually tried to do is solve the actual value of "w" using the quadratic equation. However, when I plug this into the 2nd equation, this yields "3", when the answer is 2.
Also, no calculators are allowed on the exam, so I can't be using the quadratic equation.
Any help is appreciated.
Thanks.