Let ω (ω ≠ 1) is a cube root of unity, such that (1+ω2)8 , where a,b∈ R, then |a + b| is equal to

Question

Let ω (ω ≠ 1) is a cube root of unity, such that (1+ω2)8 , where a,b∈ R, then |a + b| is equal to (A) 1 (B) 3 (C) 0 (D) 2

Tardigrade Admin · Accepted Answer

We have, (- ω )8=a+bω ⇒ ω2=a+b ω . ⇒ -(1/2)-i(√3/2)=a+b(- (1/2) + i (√3/2)) Comparing real and imaginary parts a=-1,b=-1 ⇒ |a + b|=2

Q. Let $ω (ω \neq = 1)$ is a cube root of unity, such that $(1 + ω^{2})^{8}$ , where $a, b \in R,$ then $∣ a + b ∣$ is equal to