Intuitively, a conformal mapping is a “mapping that preserves angles between curves”.

If \(f:U \rightarrow \mathbb{C}\) is analytic and if \(z_0 \in U\) such that \(f′(z_0) \not = 0\), then \(f\) is conformal at \(z_0\) !

Observe the contrapositive: if a function \(f\) is not conformal, then either \(f\) is not analytic or \(f′(z_0) = 0\). This means it would fail the Cauchy-Riemann equations ! The function \(\overline z\) is a good example.

# posted by rot13(Unafba Pune) @ 11:21 PM