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

Answers (1)

Solution:     Given  ,    left | z-i 
ight |< 1

         Now  ,       left | z+12-6i 
ight |=left | (z-i)+(12-5i) 
ight |

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

           ecause                           left | z_1+z_2 
ight |leq left | z_1 
ight |+left | z_2 
ight |

         Hence            left | z+12-6i 
ight |< 14.

                       

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