ToolBench
Tools
Complex Number Calculator

Complex Number Calculator

Inputs

z₁ = a + bi
+ i
z₂ = c + di
+ i
n (power for z₁ⁿ)

Operations

z₁ Analysis

Conjugate z̄₁ 3 − 4i
Modulus |z₁| 5
Argument θ (rad) 0.9273
Argument θ (deg) 53.1301
Polar form 5(cos 0.9273 + i sin 0.9273)
Exponential form 5e^(i0.9273)

Result

z₁ + z₂
4 + 2i

Argand Plane

Points are plotted with automatic scaling — vectors from the origin to z₁, z₂, and the latest result.

Formulas Used

Multiplication (a+bi)(c+di) = (ac−bd) + (ad+bc)i
Division z₁÷z₂ = z₁z̄₂ / |z₂|²
Modulus |z| = √(a² + b²)
Argument θ = atan2(b, a)
De Moivre zⁿ = rⁿ(cos nθ + i sin nθ)