If $| z - i | < 1$ , then $| z + 12 - 6 i |$

< 14

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< 16

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> 14

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= 14

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Solution

The correct option is A $< 14$
Given $| z - i | < 1$
Now $| z + 12 - 6 i | = | (z - i) + (12 - 5 i) |$
$\leq | z - i | + | 12 - 5 i | [∵ | z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |]$
$< 1 + 13 = 14$
Hence $| z + 12 - 6 i | < 14$

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