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