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AP EAMCET202022 Sep 2020Evening ShiftMathematicsComplex NumberActual

If | z-25 z-1 |=5 , then |z|=

Options

  1. A5
  2. B3
  3. C4
  4. D10

Correct answer

A. 5

Step-by-step solution

| z-25 z-1 |=5 Let z=x+i y array r | x+i y-25 x+i y-1 |=5 |(x-25)+i y| |(x-1)+i y| =5 (x-25)^2+y^2 (x-1)^2+y^2 =5 array Squaring on both sides, aligned & (x-25)^2+y^2=25 [(x-1)^2+y^2 ] & x^2+625-50 x+y^2=25 [x^2+1-2 x+y^2 ] & x^2+y^2-50 x+625=25 x^2+25 y^2-50 x+25 & 24 x^2+24 y^2=600 aligned aligned & & x^2+y^2 & =25 & & |z| & = x^2+y^2 = 25 & & |z| & =5 aligned Hence, option (1) is correct.

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