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

6 years ago


Answers : (1)


Dear Sakshi,



        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


        Þ |z1|+|z2|+|z3| <12

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

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thanks and regards.

Akhilesh Shukla

6 years ago

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