+0

# Complex Numbers

0
32
1

Let $$a, b, c, d$$ be real numbers, none of which are equal to $$-1$$, and let w be a complex number such that $$w^3=1$$ and $$w \neq 1.$$

If $$\frac{1}{a + w}+\frac{1}{b + w}+\frac{1}{c + w}+\frac{1}{d + w}= \frac{2}{w}$$, then find $$\frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c +1} + \frac{1}{d + 1}$$.

Thanks for any help, I know that by factorizing the w^3=1, you can solve for w, but this does not seem to do anything to help simplify.

May 29, 2021

#1
+556
+1

$\omega$ is a cube root of unity so write it in exponential form everywhere. This problem is easy to guess as well.

May 30, 2021