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If Real ((2z-1)/(z+1))=1, then locus of ...

If Real `((2z-1)/(z+1))`=1, then locus of z is , where z=x+iy and `i=sqrt(-1)`

A

circle

B

parabola

C

St. line

D

Pair of ST. lines

Text Solution

Verified by Experts

The correct Answer is:
A
`((2z-1)/(z+1))=((2x-1)+2iy)/((x+1)+yi)=(((2x-1)+2iy)((x+1)-iy))/((x+1)^(2)+y^(2))`
Real part`=1implies (2x-1)(x+1)+2y^(2)`
`implies 2x^(2)+x-1+2y^(2)=1`
`2x^(2)+2y^(2)+x-2=0" "therefore`Circle.
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