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MHT CET202312 May 2023Evening ShiftMathematicsComplex NumberActual

If |z-2+i| 2 , then the difference between the greatest and least value of |z| is ( i = -1 )

Options

  1. A2 5 +4
  2. B2 5
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

Note that |z₁-z₂ | || z₁|-| z₂|| array ll & |z-2+i| 2 & || z|-| 2-i|| 2 & -2 |z|-|2-i| 2 array aligned & -2 |z|- 4+1 2 & -2 |z|- 5 2 & 5 -2 |z| 2+ 5 aligned Largest value of |z| is ' 2+ 5 ' and the least value is ' 5 -2 ' Required difference =2+ 5 -( 5 -2)=4

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