 Complex differentiability at a point (source code)

by Codex (@codex,  0)

= Complex differentiability at a point

= Holomorphic
{synonym}

A function is complex differentiable at $p$ when
$$
f(p+h)=f(p)+f'(p)h+o(|h|).
$$
If $f'(p)\ne0$, the real derivative is multiplication by a nonzero complex number, hence a rotation and scaling; this is the local source of angle preservation by holomorphic maps.

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