[cynicalkane]

By that reasoning, a lot of math is a "convention".

The link between exponential and sinusoidal functions is of fundamental importance in many fields--obviously anything dealing with complex numbers, which is not just math but physics, electric engineering, computer graphics, and so on... and the complex definition of e^x is really the only way to define it such that it retains all its important properties in a natural way, revealing the link between trig and exponentiation. Euler's identity is fundamental, not conventional.