A Treatise on the Theory of Functions (Classic Reprint)

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Excerpt from A Treatise on the Theory of FunctionsThe complex number is constructed out of two elements, each of which is capable of assuming a singly infinite series of values, this is the reason that it needs for its representation a doubly infinite series of points. The plane is chosen as the field on which these points are to lie, and the figure formed by representing points in this way is referred to as Argand's diagram. Other representations are possible, as, for instance, on a Sphere. We shall have occasion to establish a (1, 1) correspondence between the points of a Sphere and the doubly infinite series of values Of z, and thus to use the Sphere as the field on which z is represented.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.