The Complex Plane

Numbers as points

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

• $a + bi$ is the point $(a, b)$ in the complex plane.
• Modulus $|z| = \sqrt{a^2 + b^2}$. Adding complex numbers adds vectors.
• $z\bar z = |z|^2$.

Steps

1. A 2D number line
2. Modulus
3. Conjugate
4. Multiplying
5. Adding is easy
6. Distance