The Square Root of −1

Meet i

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

• $i^2 = -1$. Complex numbers have the form $a + bi$.
• Do arithmetic as usual, replacing $i^2$ with $-1$.
• The powers of $i$ cycle with period 4: $i, -1, -i, 1$.

Steps

1. No solution?
2. Imaginary and complex numbers
3. Powers of i
4. Multiply
5. Powers of 1 + i
6. A big power