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JEE Main2009MathematicsComplex NumberActual

If |z- 4 z |=2 , then the maximum value of |z| is equal to

Options

  1. A3 +1
  2. B5 +1
  3. C2
  4. D2+ 2

Correct answer

B. 5 +1

Step-by-step solution

aligned & |z|= | (z- 4 z )+ 4 z | |z|= |z- 4 z + 4 z | & |z| |z- 4 z |+ 4 |z| |z| 2+ 4 |z| aligned aligned & |z|^2-2|z|-4 0 & (|z|-( 5 +1))(|z|-(1- 5 )) 0 1- 5 |z| 5 +1 aligned

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