The maximum value of |z| when z satisfies the condition |z + 2/z| = 2 is ?
Samir Madan , 11 Years ago
Grade 12
Algebra> The maximum value of |z| when z satisfies...
1 Answers
bharat bajaj
Last Activity: 11 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| -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
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IIT Delhi
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