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the complex number z satisfies th equality |z-1/z| =2 then the greatest value of |z|

the complex number z satisfies th equality
|z-1/z| =2 then the greatest value of |z|

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1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
9 years ago
Let the conjugate of complex number z be denoted by z’

Given, | z – 1/z | = 2
| z – 1/z |2 = 4,
( z – 1/z )( z’ – 1/z’ ) = 4,
zz’ – z/z’ – z’/z – 1/zz’ = 4,
|z|2+ 1/|z|2–z/z’ – z’/z = 4
|z|2+ 1/|z|2– (z2+ z’2) /|z|2= 4,
|z|2+ 1/|z|2– 2|z|2/|z|2= 4,
Solve this and get the answer.

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