if |z₁-z₂|<1,|z₂-2|<2,|z₃-3|<3 then| |z₁+z₂+z₃|

Dear Sakshi,

Since,|z₁|-1|<1

        Þ |z₁|-|1|<1         {Triangle Inequality}

        Þ |z₁|<2             ……….(1)

        Similarly, |z₂-2|<2

        Þ |z₂|<4             ………(2)

        And |z₃-3|<3

        Þ |z₂| <6            ……….(3)

        Adding (1), (2), (3), we have

        |z₁|+|z₂|+|z₃|<2+4+6

        Þ |z₁|+|z₂|+|z₃| <12

        Also, |z₁+z₂+z₃| £ |z₁|+z₂|+|z₃|<12

        \ |z₁+z₂+z₃| < 12

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