There’s something delightfully physicsy about deriving Euler’s identity, which famously deals with the irrational and the imaginary, by brute force calculation

There’s something delightfully physicsy about deriving Euler’s identity, which famously deals with the irrational and the imaginary, by brute force calculation using log tables and fudging the fifth decimal place. But the approach of sneaking backwards into the algebraic continuation of e^x by actually doing the arithmetic is a great way to viscerally get that it’s all just the same set of mathematical tools.