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

Let z∈C with Im(z)=10 and it satisfies 2 z-n2 z+n=2i-1 for some natural number n. Then
  1. n=20 and Re(z)=10
  2. n=40  and  Re(z)=10
  3. n=20 and Re(z)=-10
  4. n=40 and Re(z)=-10

Solution

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

Asked in: JEE Main 2019 (12 Apr Shift 2)

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