if |z 1 -z 2 | 2 -2| 3 -3| 1 +z 2 +z 3 |

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


1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
12 years ago

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

        \ |z1+z2+z3| < 12 provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series.

Click here to find IIT JEE Packages or course details with askIITians.

for further details visit the folowing links:

Askiitians provide you all the best possible information, feel free to ask.

all the best.

thanks and regards.

Akhilesh Shukla

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy


Get your questions answered by the expert for free