Complex Number Calculator
MathematicsPerform arithmetic operations on complex numbers (a + bi). Compute modulus |z|, argument θ (phase angle), complex conjugate, polar form (r∠θ), and Euler form.
About this calculator
Complex numbers are indispensable in electrical AC circuit impedance calculations, signal processing Fourier transforms, quantum mechanics wavefunctions, and fluid dynamics.
This calculator supports addition, subtraction, multiplication, division, and power operations on Cartesian complex numbers (a + bi), translating them into polar coordinates (r, θ) in degrees and radians.
How It Works & Formula
Modulus |z| = √(a² + b²); Argument θ = atan2(b, a). Multiplication (a+bi)(c+di) = (ac-bd) + (ad+bc)i; Division multiplies numerator and denominator by the complex conjugate (c - di).
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