We wish to examine the notion of a “function of z” where z is a complex variable. To be sure, a complex variable can be viewed as nothing but a pair of real variables so that in one sense a function of z is nothing but a function of two real variables. This was the point of view we took in the last section in discussing continuous functions. But somehow this point of view is too general. There are some functions which are “direct” functions of z = x + iy and not simply functions of the separate pieces x and y.