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## Main Question or Discussion Point

Using converse of alternate segment theorem (i think it is)

i.e. this:

"If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle"

establish the cartesian equation, range and domain of the locus of points:

Arg(z - a) - Arg(z) = pi/2

a = 1 + 0i

and for

Arg(z) - Arg(z-a) = pi/2

a = 1 + 0i

say z = x + iy ( i think )

i get

( x - 1/2 ) ^2 + y^2 = 1/4

But i'm not sure about the domain, range etc

If anyone could help me, or point me in the right direction, that would be great.

Thanks.

i.e. this:

"If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle"

establish the cartesian equation, range and domain of the locus of points:

Arg(z - a) - Arg(z) = pi/2

a = 1 + 0i

and for

Arg(z) - Arg(z-a) = pi/2

a = 1 + 0i

say z = x + iy ( i think )

i get

( x - 1/2 ) ^2 + y^2 = 1/4

But i'm not sure about the domain, range etc

If anyone could help me, or point me in the right direction, that would be great.

Thanks.