Complex Numbers And Quadratic Equations question 245
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]
Options:
A) 0
B) 1
C) $ -1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ (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
BETA
