Complex Numbers And Quadratic Equations question 265
Question: If $ \omega $ is an nth root of unity, other than unity, then the value of $ 1+\omega +{{\omega }^{2}}+…+{{\omega }^{n-1}} $ is [Karnataka CET 1999]
Options:
A) 0
B) 1
C) $ -1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ 1+\omega +{{\omega }^{2}}+…..+{{\omega }^{n-1}}=( \frac{{{\omega }^{n}}-1}{\omega -1} )=0 $ , $ (\because {{\omega }^{n}}=1) $
BETA
