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Equation of Conics in Complex Form

If |z1| = 2, ...

Question

If $| z_{1} | = 2, & z_{2}$ be the point in which sartisfies the condition $(z_{2} +_{2}) - i (z_{2} -_{2}) = 8 \sqrt{2},$ then the minimum value of $| z_{1} - z_{2} |$ is

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Solution

$| z_{1} | = 2 \Rightarrow x^{2} + y^{2} = 4 (z_{2} +_{2}) - i (z_{2} -_{2}) = 8 \sqrt{2} \Rightarrow x + y = 4 \sqrt{2}$
$A B = O B - r A B = 2$

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z_{1} = 5 + 12 i

| z_{2} | = 4

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are three points lying on the circle

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then the minimum value of

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