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Quantitative Aptitude

Solving Inequalities

|Z1|=2 and ...

Question

$| Z_{1} | = 2$ and $| Z_{2} - - 6 - 8 i = 4 |$ , then the maximum distance between $Z_{1}$ and $Z_{2}$ is:

A

10

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B

6

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C

2

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D

2 \sqrt{41} - 2

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Solution

The correct option is D $2 \sqrt{41} - 2$
$Z_{1} - 6 - 8 i = 4$
$x + i y - 6 - 8 i = 4$
$x - 6 + i (y - 8) = 4$
$x = 10, y = 8$
$Z_{2} = 10 + 8 i$
$| Z_{2} | = \sqrt{10^{2} + 8 i^{2}}$ $= 2 \sqrt{41}$
$| Z_{2} - Z_{1} | \geq | | Z_{2} | - | Z_{1} | |$
$⟹ 2 \sqrt{41} - 2$

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| Z_{1} | = 2

| Z_{2} - 6 - 8 i | = 4

, then the minimum distance between

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| Z_{2} - 6 - 8 i | = 4

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