Question

if w is a complex cube root of unity find the value of the following​

Answer 1

Step-by-step explanation:

If w is a complex root of unity then it should satisfy

${x}^{2} + x + 1 = 0$

Hence

${w}^{2} + w + 1 = 0 = > {w}^{2} + 1 = - w$

So we need to find the value of

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

Hope it helps you.