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Let Z₁ and Z₂ be two complex numbers satisfying $|Z_{1}| = 9$ and $|z_{2} - 3 - 4 i| = 4$ then the minimum value of $|Z_{1} - Z_{2}|$ is :

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$\sqrt{2}$

answer is A.

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Detailed Solution

$|Z_{1}| = 9, |z_{2} - 3 - 4 i| = 4$
C₁(0,0) radius r₁ = 9
C₂ (3,4) , radius r₂ = 4
$C_{1} C_{2} = |r_{1} - r_{2}| = 5$
$∴$ circle touches internally
$∴$ ${|z_{1} - z_{2}|}_{min} = 0$

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