e^(i*π) = -1

Also, anything like a^(log(c) / log(a)), for positive rational c and irrational a, to generalize bean_jamming’s answer

I also assert without proof that in the equation x^x = c, x is irrational for most rational values of c

I did start trying out stuff with sqrt(2), thinking back to the tower power problems, but didn’t end up coming up with your solution while doing so ¯\_(ツ)_/¯