Verified Solution • 2025–26 Session moderate

QJEEM19Maceb1: JEE Main 2019 Mathematics - Class 11 JEEM19Maceb1 Solution: Let z C with Im(z) = 10 and it satisfies = 2i - 1 for some…

Let z ∈\in C with Im(z) = 10 and it satisfies 2z−n2z+n{{2z - n} \over {2z + n}} = 2i - 1 for some natural number n. Then :

Multiple Choice Options

  • A n = 20 and Re(z) = –10
  • B n = 40 and Re(z) = 10
  • C n = 40 and Re(z) = –10
  • D n = 20 and Re(z) = 10

Step-by-Step Verified Solution

Let Re (z) = x, then

2(x+10i)−n2(x+10i)+n=2i−1{{2(x + 10i) - n} \over {2(x + 10i) + n}} = 2i - 1

⇒(2x−n)+20i=−(2x+n)−40−20i+2ni\Rightarrow \left( {2x - n} \right) + 20i = - \left( {2x + n} \right) - 40 - 20i + 2ni

⇒2x−n=2x−n−40\Rightarrow 2x - n = 2x - n - 40

& 20 = -20 + 2n ⇒\Rightarrow x = -10 & n = 20

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