Question

If w is the cube root of unity then find the value of
$\Big(\frac{-1+i\sqrt{3}}{2}\Big)^{18} + \Big(\frac{-1-i\sqrt{3}}{2}\Big)^{18}$

Answer 1

Answer:

2

Step-by-step explanation:

Hi,

w is the cube root of unity,

Let w = (-1 + i√3)/2

and then w² = (-1 - i√3)/2

Also, we know that w³ = 1

Consider the given expression

[(-1 + i√3)/2]¹⁸ + [(-1 - i√3)/2]¹⁸

= (w)¹⁸ + (w²)¹⁸

= (w³)⁶ + (w³)¹²

= 1⁶ + 1¹²

= 1 + 1

= 2

Hope, it helps !