Question

If $\omega$ is a complex cube root of unity, then (1 + $\omega$)(1 + ${\omega }^2$) $(1+{\omega }^4$) $(1+{\omega }^8$)... to 2n factors =
[AMU 2000]

• A. 1
• B. -1
• C. None of these

Answer 1

The correct option is A 1

(1 + $\omega$)(1 + ${\omega }^2$)(1 + ${\omega }^4$)(1 + ${\omega }^8$).... upto 2n factors
= (- ${\omega }^2$)(- $\omega$)(1 + $\omega$)(1 + ${\omega }^2$).... upto 2n factors
= 1.1.1.... upto n factors = 1