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The maximum value of |z| when z satisfies the condition |z + 2/z| = 2 is ?

The maximum value of |z| when z satisfies the condition |z + 2/z| = 2 is ?

Grade:12

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,

|z| = |z +2/z - 2/z|_max = |z+2/z| + |2/z|
=>|z|_max = 2 + |2/z|
=>|z|^2 - 2|z| -2 = 0
=>|z|^2 - 2|z| +1 = 3
=>(|z| - 1)^2 = 3
=>|z| - 1 = root3
=>|z|_max=1+root3
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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