I like Feynman's description, where he actually used 10^x first, just noting that 10^x for small real x was 1 + ln(10)*x (approximating from the derivative), as

I like Feynman's description, where he actually used 10^x first, just noting that 10^x for small real x was 1 + ln(10)*x (approximating from the derivative), assuming that this worked for small complex values too, and then extended to larger values by squaring.