Let \( C_{1} \) and \( C_{2} \) are concentric circles of radius 1 and \( 8 / 3 \) respectively ... VIDEO
Let \( C_{1} \) and \( C_{2} \) are concentric circles of radius 1 and \( 8 / 3 \) respectively having centre at \( (3,0) \) on the argand plane. If the complex number \( z \) satisfies the inequality,
\( \log _{1 / 3}\left(\frac{|z-3|^{2}+2}{11|z-3|-2}\right)1 \) then:
(a) \( z \) lies outside \( C_{1} \) but inside \( C_{2} \)
(b) \( z \) lies inside of both \( C_{1} \) and \( C_{2} \)
(c) \( z \) lies outside both of \( C_{1} \) and \( C_{2} \)
(d) none of these.
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