If locus of z is a curve satisfying |z−(3+2i)|=Re⁡(z) and z1&z2 are two point on the curve such  that arg⁡z1−(3+2i)z2−(3+2i)=π then

let z=x+iyRe⁡z=x distance of z from fixed point (3+2i)= distance of z from fixed  line (y−axis)⇒ locus of z is parabola with focus 3+2i, and directrix y-axis. arg⁡z1−(3+2i)z−(3+2i)=π⇒z1,(3+2i),z2  are collinear and  hence z1z2 are extrimites of focal chord.  Circle with z1z2 as diameter touch the directrix hence at  corresponding point of contact z1z2 subtend 90∘ and at other  points of directrix (out side point to the circle), z1z2 subtend less  than 90∘.