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AP EAMCET20226 Jul 2022Evening ShiftMathematicsComplex NumberActual

For any complex number z , the minimum value of |z|+|z-1| is

Options

  1. A1
  2. B0
  3. C1 / 2
  4. D3 / 2

Correct answer

A. 1

Step-by-step solution

Let z=x+i y aligned |z| & = x^2+y^2 |z-1| & = (x-1)^2+y^2 = x^2-2 x+1+y^2 aligned For minimum value of |z| and |z-1| aligned & |z-1| 0 & x-1 0 [ y^2 0 ] & x 1 aligned The minimum value of |z|+|z-1| is 1 .

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