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Complex Plane

For all compl...

Question

For all complex numbers $z_{1}, z_{2}$ such that $| z_{1} | = 12$ and $| z_{2} - 3 - 4 i | = 5$ , the minimum value of $| z_{1} - z_{2} |$ is

A

0

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B

2

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C

7

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D

10

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Solution

The correct option is B $2$
Minimum distance will be along lines joining two center
$= R_{1} - 2 R_{2}$
$= 12 - 2 \times 5 = 2$ units

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