Abstract
In order to visualize the complex values of y, when such exist, of a plane curve y=f(x), or a surface y=f(x, z), and also for the purpose of representing some real curves in space by a single independent equation in x and y, I adjoin an ordinary complex plane, perpendicular to the x axis of the real xy plane, with its real axis parallel to the y axis, in fact always in the real plane and with its origin in the axis of x, so that the complex plane slides along always perpendicular to the x axis, OX, and at distance x from O the origin of the xy plane, as x changes. By this representation the equation of every curve or surface has an actual and uninterrupted locus from − ∞ to + ∞, including the usual real locus of y = f (x) or y = f (x, z), and some real curves in space can be represented by a single independent equation between two variables x and y.
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