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JEE Main201912 Apr 2019Evening ShiftMathematicsComplex NumberActual

Let z ∈ C with I m ( z ) = 10 and it satisfies 2   z - n 2   z + n = 2 i - 1 for some natural number n . Then

Options

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

Correct answer

D. n = 40 and R e ( z ) = - 10

Step-by-step solution

Put z = x + 10 i ∴ 2 x + 10 i - n = 2 i - 1 ⋅ 2 x + 10 i + n compare real and imaginary coefficients x = - 10 , n = 40

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