Complex Plane Navigation

Trigonometry · Axiom Academy

Discover how complex numbers create a two-dimensional number system and connect to the trigonometry you know! A complex number has two parts: a real part and an imaginary part . We write them as a + bi . Click anywhere on the plane to plot a complex number! Every complex number has a distance from the origin (called magnitude or modulus) and a direction (angle). Use the sliders to explore! Instead of a + bi , we can write complex numbers using distance and angle: r(cos θ + i sin θ) Here's the magic: a = r cos θ and b = r sin θ . The complex plane is built on right triangles!

This is the written version of the interactive lesson above. See the full Trigonometry course.