# Let $z\epsilon C$  with $Im(z)=10$  and  it satisfies $\frac{2z-n}{2z+n}=2i-1$  for some natural number n . Then :  Option 1)  n = 20 and Re(z) = -10 Option 2)  n = 40 and Re(z) = 10 Option 3)  n = 40 and Re(z) = -10 Option 4)  n = 20 and Re(z) = 10

$\frac{2z-n}{2z+n}=2i-1$ , $z\epsilon C$ , $Im(z)=10$

$\\let\;z=x+10i\\\frac{2(x+10i)-n}{2(x+10i)+n}=2i-1\\2x-n+20i=(2i-1)(2(x+10i)+n)=(2i-1)((2x+n)+20i)\\2x-n+20i=4xi+2ni-40-2x-n-20i\\2x-n+20i=(-40-2x-n)+i(4x+2n-20)\\compare\;real\;and\;img\;part\\2x-n=-40-2x-n\\20=4x+2n-20\\x=-10\\n=40$

Option 1)

n = 20 and Re(z) = -10

Option 2)

n = 40 and Re(z) = 10

Option 3)

n = 40 and Re(z) = -10

Option 4)

n = 20 and Re(z) = 10

### Preparation Products

##### Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
##### Rank Booster JEE Main 2020

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 9999/- ₹ 4999/-
##### Test Series JEE Main Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 1999/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-