Multiplying Rotates

Lengths multiply, angles add

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

• Multiplying by $i$ rotates by 90°.
• In general: lengths multiply and angles add.
• Polar form: $z = r(\cos\theta + i\sin\theta)$.

Steps

1. Times i
2. Multiply two numbers
3. Polar form
4. Angle of a product
5. Back to the start
6. Repeated multiplication