%%visits: 5 This is a generalisation of [[integral]] on the “[[complex_number]] line”. It allows us to calculate real integrals much easier then without them.
Complex functions take (x, y) and map them to (x, y), so there are 4 dimensions to the integral, and the bounds are typically 2d shapes, hence visualising them are no longer thought about as a way to understand them. %% ==intuition %% ==rigour ## exam clinic 1. First thing to note is that if the function is [[holomorphic]] in all of the region, then the integral is 0. 2. [[Cauchys_integral_formula]] or [[Cauchys_residue_theorem]], Goursats_theorem 3. Parameterisations.
Fundamental estimate would come last, it is really mainly used when making proofs %% ==examples and non-examples %% ==related tags math