On imaginary expressions and their moduli.

Chapter
Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)

[153] In analysis, we call a symbolic expression or symbol any combination of algebraic signs that do not mean anything by themselves or to which we attribute a value different from that which they ought naturally to have. Likewise, we call symbolic equations all those that, taking the letters and the interpretations according to the generally established conventions, are inexact or do not make sense, but from which we can deduce exact results by modifying and altering either the equations themselves or the symbols which comprise them, according to fixed rules. The use of symbolic expressions or equations is often a means of simplifying calculations and of writing in a short form results that appear quite complicated. We have already seen this in the second section of the third chapter where formula (9) gives a very simple symbolic value to the unknown x satisfying equations (4).1 Among those symbolic expressions or equations which are of some importance in analysis, we should distinguish above all those which we call imaginary. We are going to show how we can put them to good use.

Keywords

Integer Number Fractional Power Positive Quantity Negative Power Imaginary Root