Euler’s Formula

e^(iπ) + 1 = 0

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Euler's formula: $e^{i\theta} = \cos\theta + i\sin\theta$.
• $e^{i\pi} + 1 = 0$.
• Any complex number is $re^{i\theta}$: a length times a rotation.

Steps

1. Exponentials that rotate
2. Half a turn
3. Quarter turn
4. A sixth of a turn
5. Length of an exponential
6. i to the i