What is Euler’s formula actually saying? | Ep. 4 Lockdown live math

What does it mean to compute e^{pi i}? Full playlist: Home page: Brought to you by you: Beautiful pictorial summary by @ThuyNganVu: Not on the “homework“ to show that exp(x y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about whether the series really converge, what they converge to, and how exactly you define a product with infinitely many terms. For anyone curious about the technical details, what you would want to show is that the Cauchy Product of the series for exp(x) and exp(y) converges to the product of the values exp(x) and exp(y) for any particular x and y. That requires the Merten’s Theorem. ------------------ Video Timeline (Thanks to user “Just TIEriffic“