Let z(t) = x(t) + ≀y(t), a ≤ t ≤ b, be a path. We suppose throughout this chapter that z′(t) ≠ 0 for all t. Let f be defined in a neighborhood of a point z 0 ∈ ℂ. f is conformal at z 0 if f preserves angles at z 0, for any two paths P 1 and P 2 intersecting at z 0 the angle from P 1 to P 2 at z 0, the angle oriented counterclockwise from the tangent line of P 1 at z 0 to the tangent line of P 2 at z 0, is equal to angle between f(P 1) and f(P 2). The function f is conformal in a region O if it is conformal at all points from O.
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