JEE Main2017MathematicsComplex NumberActual
Let ω be a complex number such that 2 ω + 1 = z where z = - 3 . If 1 1 1 1 - ω 2 - 1 ω 2 1 ω 2 ω 7 = 3 k , Then k can be equal to:
Options
- A– z
- B1 z
- C- 1
- D1
Correct answer
A. – z
Step-by-step solution
ω =   - 1 2 + 3 2   i (cube root of unity) So, 1 + ω + ω 2 = 0 and ω 3 =1 Now 1 1 1 1 ω ω 2 1 ω 2 ω = 3 ω 2 - ω So k = ω 2 - ω ⇒ k = - 1 2 - 3 2 i - - 1 2 + 3 2 i ⇒ k = - 3 i ⇒ k = - z