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Let Z in C with Im (z) = 10 and it satis...

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

Text Solution

Verified by Experts

The correct Answer is:
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
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