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Manipal MET2022MathematicsComplex Number

If |z+ 2 z |=2 , then the minimum value of |z| is

Options

  1. A1+ 2
  2. B1+2 2
  3. C3 3 +1
  4. D1- 3

Correct answer

D. 1- 3

Step-by-step solution

We can write aligned & |z|= |z+ 2 |z| - 2 |z| | |z+ 2 z |+ | 2 |z| | & =2+ 2 |z| & |z|^2-2|z|-2 0 aligned Here, |z| lies between 2 12 2 =1 3 Minimum value of |z|=1- 3

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