Search any question & find its solution
Question:
Answered & Verified by Expert
If $\omega$ is a complex cube root of unity, then what is the value
of $1-\frac{1}{(1+\omega)}-\frac{1}{\left(1+\omega^{2}\right)} ?$
Options:
of $1-\frac{1}{(1+\omega)}-\frac{1}{\left(1+\omega^{2}\right)} ?$
Solution:
1500 Upvotes
Verified Answer
The correct answer is:
0
$1-\frac{1}{(1+\omega)}-\frac{1}{\left(1+\omega^{2}\right)}=1-\frac{1}{-\omega^{2}}-\frac{1}{-\omega}$
$=\frac{\omega^{2}+1+\omega}{\omega^{2}}=\frac{0}{\omega^{2}}=0$
$=\frac{\omega^{2}+1+\omega}{\omega^{2}}=\frac{0}{\omega^{2}}=0$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.