Matrices and Determinants 1 Question 16
16. Let $\omega$ be a solution of $x^{3}-1=0$ with $\operatorname{Im}(\omega)>0$. If $a=2$ with $b$ and $c$ satisfying Eq. (i) then the value of $\frac{3}{\omega^{a}}+\frac{1}{\omega^{b}}+\frac{3}{\omega^{c}}$ is
(a) -2
(b) 2
(c) 3
(d) -3
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Answer:
Correct Answer: 16. (a)
Solution:
- If $a=2, b=12, c=-14$
$\therefore \frac{3}{\omega^{a}}+\frac{1}{\omega^{b}}+\frac{3}{\omega^{c}}$
$\Rightarrow \frac{3}{\omega^{2}}+\frac{1}{\omega^{12}}+\frac{3}{\omega^{-14}}=\frac{3}{\omega^{2}}+1+3 \omega^{2}=3 \omega+1+3 \omega^{2}$
$ =1+3\left(\omega+\omega^{2}\right)=1-3=-2 $
