Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 201912 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 12 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Complex Number

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Complex Number

Let z ∈ C with Im ( z ) = 10 and it satisfies (2z - n)/(2z + n) =...

Let

z \in C

with

Im ( z ) = 10

and it satisfies

\dfrac{2z - n}{2z + n} = 2i - 1

for some natural number

n .

Then

Options

A $n = 20$ and $Re ( z ) = 10$
B $n = 40$ and $Re ( z ) = 10$
C $n = 20$ and $Re ( z ) = - 10$
D $n = 40$ and $Re ( z ) = - 10$

Correct answer

D. $n = 40$ and $Re ( z ) = - 10$

Step-by-step solution

Put

z = x + 10i

∴ 2

\left(x + 10i\right) - n = \left(2i - 1\right) ⋅ \left[2\left(x + 10i\right) + n\right]

<br/>compare real and imaginary coefficients <br/>

x = - 10, n = 40

Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z ∈ ℂ , satisfying the equations |z-(4+8i)|= 10 and… JEE Main 2026 Let S = \ z ∈ ℂ : z^2 + 6 \,iz - 3 = 0\ . Then ∑ _ z ∈ S z^8 is equal to : JEE Main 2026 Let the set of all values of k ∈ ℝ such that the equation z( z + 2 + i) + k(2 + 3i) = 0… JEE Main 2026 Let z_1, z_2 ∈ ℂ be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 .… JEE Main 2026 Let S=\ z ∈ ℂ: z^2+4z+16=0\ . Then ∑_ z ∈ S |z+ 3 i|^2 is equal to: JEE Main 2026 Let z be a complex number such that |z+2| = |z-2| and ((z+3)/(z-i)) = (π)/(4) . Then… JEE Main 2026 Let the circles C_1 : |z| = r and C_2 : |z - 3 - 4i| = 5 , z ∈ ℂ , be such that C_2 lies… JEE Main 2026 Let x and y be real numbers such that 50((2x)/(1+3i) - (y)/(1-2i)) = 31 + 17i , i = -1 .… JEE Main 2026 Let A=\ z ∈ ℂ:|z-2| 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the max \ |z_ 1 -z_ 2 |: z_ 1… JEE Main 2026 Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5 . Then the value of z^ 3 +3… JEE Main 2026 Let z=(1+i)(1+2 i)(1+3 i) …(1+n i) , where i= -1 . If |z|^ 2 =44200 , then n is equal to… JEE Main 2026 If z= 3 2 +(i)/(2), i= -1 , then (z^ 201 -i)^ 8 is equal to JEE Main 2026 Let S=\ z: 3 |2 z-3(1+i)| 7\ be a set of complex numbers. Then _ z ∈ S |(z+(1)/(2)(5+3… JEE Main 2026 Let S=\ z ∈ ℂ: 4 z^ 2 + z =0\ . Then ∑_ z ∈ S |z|^ 2 is equal to: JEE Main 2026 Let α= -1+i 3 2 and β= -1-i 3 2 , i= -1 . If (7-7 α+9 β)^ 20 +(9+7 α-7 β)^ 20 +(-7+9 α+7… JEE Main 2026 Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal… JEE Main 2026 Full Complex Number list Complex Number JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs