How do you mean? Euler's identity comes from Euler's formula and that's just a way to rewrite your number into a more convenient base but it's still very much a

How do you mean? Euler's identity comes from Euler's formula and that's just a way to rewrite your number into a more convenient base but it's still very much a complex number? Euler's identity just happens to give 0 for the imaginary part, you can't do that for all imaginary numbers.