Let ω ω ≠ 1 is a cube root of unity, such that 1 + ω 2 8 = a + b ω where a , b ∈ R , then a + b is equal to

Question

Let ω ω ≠ 1 is a cube root of unity, such that 1 + ω 2 8 = a + b ω where a , b ∈ R , then a + b is equal to, 1, 3, 0, 2

MARKS App · Accepted Answer

- ω 8 = a + b ω ⇒ ω 2 = a + b ω … … … i ⇒ - 1 2 - i 3 2 = a + b - 1 2 + i 3 2 Comparing real and imaginary parts a = - 1 , b = - 1 ⇒ a + b = 2