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MHT CET202314 May 2023Evening ShiftMathematicsComplex NumberActual

Let z C with Im ( z )=10 and it satisfies 2 z - n 2 z + n =2 i -1, i = -1 for some natural number n , then

Options

  1. An =20 and Re ( z )=-10
  2. Bn =40 and Re ( z )=-10
  3. Cn =40 and Re ( z )=10
  4. Dn =20 and Re ( z )=10

Correct answer

B. n =40 and Re ( z )=-10

Step-by-step solution

aligned & Im ( z )=10 & Let z =x+10 i & 2 z - n 2 z + n =2 i -1 & 2(x+10 i )- n 2(x+10 i )+ n =2 i -1 & (2 x- n )+20 i =(2 i -1)(2 x+20 i + n ) & (2 x- n )+20 i =(-2 x- n -40)+(4 x+2 n -20) i aligned Equating real and imaginary parts, we get aligned & 2 x- n =-2 x- n -40 and 20=4 x+2 n -20 & x=-10 and 20=4(-10)+2 n -20 & x=-10 and n =40 aligned

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