complex variable

The variation in healthy hearts produced a very complex, variable melody line.

Consider the polynomial z2, where is the complex variable x+iy.

Of this enormously powerful relation, a more lately discovered result, which is very fundamental in the theory of functions of a complex variable, and which is generally quoted as Riemann's theorem, is only a particular case.

It will be seen that as each successive aspect of geographical science is considered in its natural sequence the conditions become 638 Conclusion. more numerous, complex, variable and practically important.

Of Functions of a Complex Variable in General.—We have in what precedes shown how to generalize the ordinary rational, algebraic and logarithmic functions, and considered more general cases, of functions expressible by power series in z.