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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

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
|z| = |z +2/z - 2/z| <= |z+2/z| + |2/z|
or, |z| <= 2 + |2/z|
|z|^2 - 2|z| -2 <= 0
|z|^2 - 2|z| +1 <= 3
( |z| - 1)^2 <= 3
|z| - 1 <= v3

Hence max. value of z is 1+v3
Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

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