Augustin-Louis Cauchy (1789-1857) initiated complex function theory in an 1814 memoir
submitted to the French Acad´emie des Sciences. The term analytic function was not
mentioned in his memoir, but the concept is there. The memoir was published in 1825.
Contour integrals appear in the memoir, but this is not a first, apparently Poisson had
a 1820 paper with a path not on the real line. Cauchy constructed the set of complex
numbers in 1847 as R[x]/(x2 + 1)