Assignment of Numerical Values to the Imaginary Unit, i, in "Identities" That Contain the Imaginary Unit

One way of looking at the imaginary unit (i, in which i = square root of -1, "derived" as a "root" or "zero" of the function y = x^2 + 1) is to say that, particularly in any expression in which i appears more than once, i cannot = itself and has to be assumed to be two different numbers. In fact, one has to define i as being some number, if one ever wants to make use of complex numbers in a real-world setting. Assuming that one does define i as being a number, one finds that, in essentially all of the i-related "identities" that contain "more than one i" [such as Euler's identity, in which e^(ix) = cos x + i(sin x)], any choice of a value of i in the e^ix term must be accompanied by a different value for i in the i(sin x) term. In other words, one has to express the identity as being e^i(i1)x = cos x + (i2)(sin x). Another way to express this would be to use y(sub)1 and y(sub)2, etc. In any case, the use of this approach allows one to find an infinite set of pairs of numbers. When one looks at different i-related identities, one gets some interesting results that I don't have the time to discuss, at the moment.