Question

If the real part of `(z +2)/(z -1)` is `4,` then show that the locus of he point representing `z` in the complex plane is a circle.

Answer 1

`z=x+iy`
`Re((Z+2)/(Z-1))=4`
`((x+iy+2)/(x+iy-1))((x-1-iy)/(x-1-iy))`
`(((x+2)+iy)/((x-1)+y)*((x-1)-iy)/((x-1)-iy))`
`((x-1)(x+2)+(iyx-iy)+i())/((x-1)^2+y^2`
`(x^2-x+2x-2+y^2)/(x^2+1-2x+y^2)`
`x^2+y^2+x-2=4x^2+4y^2-2x+4`
`3x^2+3y^2-3x+6=0`
`x^2+y^2-x+2=0`.