Complex exponentiation is not defined arbitrarily to make Euler identity true. The Euler identity is a consequence. I love the Euler identity in its typical fo

Complex exponentiation is not defined arbitrarily to make Euler identity true. The Euler identity is a consequence. I love the Euler identity in its typical form, but I think it is more surprising when you replace e and pi by their (approximate) numerical values and i by sqrt(-1)