JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let integers \(\mathrm{a}, \mathrm{b} \in[-3,3]\) be such that \(\mathrm{a}+\mathrm{b} \neq 0\). Then the number of all possible ordered pairs
(a, b), for which \(\left|\frac{z-\mathrm{a}}{z+\mathrm{b}}\right|=1\) and \(\left|\begin{array}{ccc}z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega\end{array}\right|=1, z \in \mathrm{C}\), where \(\omega\) and \(\omega^2\) are the roots of \(x^2+x+1=0\), is equal to ________.
- A 5
- B 1
- C 10
- D 9
Answer & Solution
Correct Answer
(C) 10
Step-by-step Solution
Detailed explanation
\begin{aligned} & a, b \in I,-3 \leq a, b \leq 3, a+b \neq 0 \\ & |z-a|=|z+b| \\ & \left|\begin{array}{ccc}z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega\end{array}\right|=1 \\ & \Rightarrow\left|\begin{array}{ccc}z & z & z \\ \omega & z+\omega^2 &…
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