Find the loci for the complex numbers that satisfy|z-1|=|z+1|

Question

Find the loci for the complex numbers that satisfy
`|z-1|=|z+1|`

Answer 1

Let
`z=x+iy`. Then


`|z-1|=√((x-1)^2+y^2)`

`|z+1|=√((x+1)^2+y^2)`

`\implies (x-1)^2+y^2=(x+1)^2+y^2`

`\implies (x-1)^2=(x+1)^2`

`\implies -2x=2x`

`\implies x=0`