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Question: Answered & Verified by Expert
If $\omega$ is a complex cube root of unity, then what is the value
of $1-\frac{1}{(1+\omega)}-\frac{1}{\left(1+\omega^{2}\right)} ?$
MathematicsComplex NumberNDANDA 2008 (Phase 2)
Options:
  • A 1
  • B 0
  • C $\omega$
  • D $\omega^{2}$
Solution:
1500 Upvotes Verified Answer
The correct answer is: 0
$1-\frac{1}{(1+\omega)}-\frac{1}{\left(1+\omega^{2}\right)}=1-\frac{1}{-\omega^{2}}-\frac{1}{-\omega}$
$=\frac{\omega^{2}+1+\omega}{\omega^{2}}=\frac{0}{\omega^{2}}=0$

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