Real and imaginary parts
John D. Cook discusses notes based on Henry Baker's approach to implementing complex-variable functions using real-variable functions, decomposing f(x+iy) into real and imaginary parts u(x,y) and v(x,y).
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The article shows how to build complex analytic functions from their real parts using the Schwarz reflection principle and analytic continuation, recovering a function from real-axis data up to an additive imaginary constant.