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If |z-4/z| = 2 , then the maximum value ...

If `|z-4/z| = 2` , then the maximum value of `|z|`

Text Solution

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`|z| = |z-4/z + 4/z| `
`<= |z-4/z| + |4/z|`
`|z| <= 2 + 4/|z| `
`=> |z| - 2 - 4/|z| <= 0`
`(|z|^2 - 2|z| -4)/|z| <= 0 `
roots are `|z = +- 2 + - (sqrt(4 +16))/2`
`= 1 +- sqrt5 `
`0 <= |z| <= 1 + sqrt5 `
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