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What It Means

The mathematical symbol “i” (lower case) stands for the square root of negative one, which is expressed as follows i ! - 1. It is referred to as an imaginary number since there are no real numbers, that when squared, result in a negative number. The first use of the letter i for this symbol is attributed to the mathematician, Leonhard Euler (pronounced Oiler). Euler was born in Basel, Switzerland and was famous for his exceptional output of original mathematics covering a wide range of subjects. His output even increased after he became blind in 1766. Besides his many contributions to number theory, Euler made significant contributions to the areas of calculus, geometry, algebra, probability, acoustics, optics, mechanics, astronomy, artillery, navigation, statistics, and finance.

The mathematical symbol “e” (lower case) represents the base of natural logarithms, or 2.71828… (the ellipsis denotes an irrational number, or one that cannot be written in closed form). Euler was the first to use the letter e for this constant. It has sometimes been referred to as Euler’s constant. (The term Napier's constant has also been suggested.)


When combined as in the Idea Engineering logo, it is expressed as “i to the e’th power,” or more simply, “i to the e.” Mathematically, this is referred to as a complex number, which is the sum of a real (-0.428) and an imaginary number (-0.904i) as below..

i° ª - 0.428 - 0.904i

or as we choose to say it…

The Infinite Power of the Imagined