Complex numbers · explainer

What is i?

i is a root of x² = −1. Each multiply-by-i is a 90° turn — powers cycle every four steps.

iⁿ (active) cycle points

Each ×i is a quarter-turn · scroll zoom · drag to pan

Defining equation

Show both roots
i and −i both square to −1

Power n

n = 0

Cycle

Working

Powers of i rotate by 90° each time: 1 → i → −1 → −i → 1.