Question

Let `Z in C` with Im (z) = 10 and it satisfies `=(2z-n)/(2z+n)=2i-1`
For some natural number n. then
A. n=20 and Re (z) =-10
B. n=40 and Re (z) =10
C. n=40 and Re(z)
D. n=20 and Re (z)=10

Answer 1

Correct Answer - C
Let z=x+10 I, as Im(z) = 10 ( given )
Since z satisfies
`(2z-n)/(2z +n)=2i -1 , n ne N`
`therefore (2x+20 i-n)=(2i -1)(2x+20 I +n)`
`rArr (2x-n)+20 i=(-2 -n- 40 )+(4x+2n- 20)i`
On comparing real imaginary parts ,we get
`2x-n= -2 x-n 40 and 20 = 4x+2n-20`
`rArr 4x = -40 and 20 = 4x 2n = 40 `
`rArr x=-10 and - 40 +2n = 40 rArr n = 40`
So , n = 40 and x= Re (z) = -10