‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) And ‌
z+i
z−i
=‌
x+i(y+1)
(x+1)+iy
×‌
(x+1)−iy
(x+1)−iy
Now arg(‌
z+i
z−i
)=Tan−1[‌
(x+1)(y+1)−xy
x(x+1)+y(y+1)
]=‌
Ï€
2
x2+y2x+x+y=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) Equation of common chord of circles (i) and (ii) is S1−S2=0 −3x−‌
y
2
=0 y+6x=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(III) From equation (II) and (III), the intersection of the circles is, x2+36x2+x−6x‌‌=0 x‌‌=0,‌
5
37
So the values of y are 0,−‌
30
37
This implies the point of intersection of the curves C1 and C2 other than the origin is (‌