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if the point z1=1+i where i=sqrt(-1) is ...

if the point `z_1=1+i` where `i=sqrt(-1)` is the reflection of a point `z_2=x+iy` in the line `ibarz-iz=5` then the point `z_2` is

A

`1+4i`

B

`4+i`

C

`1-i`

D

`-1-i`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `=a+bi`

`impliesbarz=a-bi`
`thereforei barz-iz=i[(a-bi)]=5`
`impliesi[-2bi]=5`
`impliesb=(5)/(2)`
So from figure it is clear that
`x=1,y=5/2+3/2=4`
`z_(2)=1+4i`
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