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18.04 Complex analysis with applications

Complex analysis with applicationsSpring 2020 lecture notesInstructor: R. R. RosalesThese notes are an adaption and extension of the original notes for by Andre Nachbinand Jeremy Orloff and later on by J orn Dunkel. Credit for course design and contentshould go to them; responsibility for typos and errors lies with will be updating and modifying the the date to make sure that you have the most current 20, 2020 Contents1 Brief course Topics needed from prerequisite math classes .. Level of mathematical rigor .. Speed of the class ..62 Complex algebra and the Complex Motivation .. Fundamental theorem of algebra .. Terminology and basic arithmetic .. The Complex plane .. geometry of Complex numbers .. triangle inequality .. Polar coordinates .. Euler s Formula .. exponential behaves like a true exponential .. exponentials and polar form.

2 Complex algebra and the complex plane We will start with a review of the basic algebra and geometry of complex numbers. Most likely you have encountered this previously in 18.03 or elsewhere. 2.1 Motivation The equation x2 = 1 has no real solutions, yet we know that this equation arises naturally and we want to use its roots.

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