Complex Plane

Plot complex numbers in rectangular or polar form, drag them on the plane, and see addition, multiplication, powers, and roots as rotation and scaling.

Unit circleVectorsAngle arcsPoint mode (click to add a number)

Show z₁

Color

3 + 4i = 5∠53.1301°

Show z₂

Color

-2

1 - 2i = 2.2361∠-63.4349°

Operations

Operation

z₁ + z₂ =

4 + 2i

Step-by-step

z₁ + z₂ = (3 + 1) + (4 + -2)i
= 4 + 2i

Forms — z₁

Rectangular: $z₁ = 3 + 4i$
Polar: z₁ = 5∠53.1301°
Trigonometric: z₁ = 5(cos 53.1301° + i sin 53.1301°)
Exponential (Euler): $z₁ = 5e^{0.9273i}$