Change in angle between curves due to stereographic projection

Suppose I have say two curves on the complex plane intersecting at a point $P$. Then is the angle between those curves at $P$ same as the angle between their spherical images on the Riemann Sphere (by the inverse of the stereographic projection) at their intersection point ? If not, then what properties those curves should satisfy to make the angles equal ?

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Thanks for the link J.M. –  pritam Aug 13 '12 at 12:30