Though Euler’s Identity follows from the polar form of complex numbers, it is impossible to derive the polar form (in particular the spontaneous appearance of the number e) without calculus.

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be ... Even ...

Benjamin Pierce, a Harvard mathematician, after proving Euler’s equation ... His works help form the foundation of nearly all areas of mathematics, including calculus, number theory, geometry ...

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be ... one equation to rule them all: Euler’s 1740 formula.