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

Solution:     Given  ,    $\left | z-i \right |< 1$

Now  ,       $\left | z+12-6i \right |=\left | (z-i)+(12-5i) \right |$

$\Rightarrow$            $\left | z+12-6i \right |\leq \left | z-i \right |+\left | 12-5i \right |$ $< 1+13=14$

$\because$                           $\left | z_{1}+z_{2} \right |\leq \left | z_{1} \right |+\left | z_{2} \right |$

Hence            $\left | z+12-6i \right |< 14.$

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