# Student Colloquium - Andreas Hagner: Complex Analysis and its use in physics

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*Supervisor: Dmitri Vladimir Fedorov*

Complex numbers were conceived of in 1545 by Italian mathematician Gerolamo Cardano to solve cubic equations as their solutions contained square roots of negative numbers. And as a (probably) physicist you might ask yourself: “What do I need complex numbers for? It’s not like I will go out and find one in nature!”.

And even though the prior statement might be true, you will need complex numbers to understand physics in full. The Schrödinger equation contains an imaginary number and because of this the wave function will be a complex and to understand complex functions we need complex analysis.

So, come to this colloquium if you want an overview of complex analysis and some of its main result, herein the ever useful residue theorem, and examples of how one might use complex analysis in physics.