JEE Advanced2011MathematicsComplex NumberActual

If z is any complex number satisfying |z-3-2 i| 2 , then the maximum value of |2 z-6+5 i| is

Correct answer

Step-by-step solution

Given, |z-3-2 i| 2 To find minimum of |2 z-6+5 i| or 2 |z-3+ 5 2 i | Using triangle inequality, i.e. || z₁|-| z₂|| |z₁+z₂ | |z-3+ 5 2 i |= |z-3-2 i+2 i+ 5 2 i |= |(z-3-2 i)+ 9 2 i | || z-3-2 i |- 9 2 | |2- 9 2 | 5 2 |z-3+ 5 2 i | 5 2 or |2 z-6+5 i| 5

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