18.03 LECTURE NOTES, SPRING 2014 - MIT Mathematics

one could not use it to de ne ez, because \eraised to a complex number" has no a priori meaning. Theorem 7.5. The complex exponential function ez has the following properties: (a) The derivative of e zis e. (b) e0 = 1. (c) ez+ w= eze for all complex numbers zand w. (d) (ez)n = enz for every complex number zand integer n. The n= 1 case says

  Number, Every, Complex, Complex number, Every complex