^{i}

Date: Tue 10.11.98 20:00

From: Alex Bogomolny

The trigonometric identity you forgot is de Moivre's formula:

https://www.cut-the-knot.com/pythagoras/cycloids.shtml#demoivre

Think of the angle for which the formula results in "i" on the left. Then raise both sides to the power of "i": i^i = e^{-Pi/2}.