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

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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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2019

MathematicsMediumsingle choice

Let $z \in C$ with $I m (z) = 10$ and it satisfies $\frac{2 z - n}{2 z + n} = 2 i - 1$ for some natural number $n .$ Then

Answer:

Solution:

Put $z = x + 10 i$
$∴ 2 (x + 10 i) - n = (2 i - 1) \cdot [2 (x + 10 i) + n]$
compare real and imaginary coefficients
$x = - 10, n = 40$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2019

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