If $| z - 1 | < 1$ , then the value of $| z + 12 - 6 i |$ is less than

14

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2

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28

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None of these

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Solution

The correct option is C $28$
$| z + 12 - 6 i |$ represents distance from $(- 12, 6)$

point at max. distance $= d (- 12, 6), (0, 0) + r a d i u s$
$= \sqrt{144 + 36} + 1$
$= 1 + \sqrt{180}$
$= 1 + 13.416$
$= 14.416$
this value is less than 28.

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