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...An introduction to complex analysis and geometry john p d angelo dept of mathematics univ illinois w green st urbana il jpda math uiuc edu c by contents chapter from the real numbers number systems inequalities ordered elds alternative denitions aglimpse at metric spaces conjugation existence square roots limits convergent innite series uniform convergence consequences unit circle trigonometry addition multiplication logarithms lines circles balls analytic quadratic polynomials linear fractional transformations riemann sphere power expansions geometric radius generating functions fibonacci application rationality dierentiation function cauchy equations orthogonal trajectories harmonic what is a dierential form integration valued line integrals goursat s proof integral formula areturn denition applications singularities residues evaluating using variables methods fourier transforms gamma additional topics minimum maximum theorem fundamental algebra winding zeroes poles pythagorean tripl...