Complex Number Calculator
Perform complex number arithmetic operations, find magnitudes, arguments, and convert between polar and rectangular forms
Complex Number Operations
First Complex Number
Second Complex Number
How to Use This Calculator
Select Operation
Choose the complex number operation you want to perform from the dropdown menu. Options include addition, subtraction, multiplication, division, magnitude, argument, conjugate, and conversions between polar and rectangular forms.
Enter Values
Input the required complex numbers. For arithmetic operations, enter both real and imaginary parts for two complex numbers. For single operations, enter one complex number. For conversions, use the appropriate input format.
View Results
The calculator will automatically compute and display the result. For arithmetic operations, you'll see the complex number result. For properties, you'll see the magnitude, argument, or conjugate. For conversions, you'll see the converted form.
Share Calculations
Use the share button to generate a link to your calculation that you can share with others. The link will preserve all your input values and results.
Complex Number Tips
A complex number is written as a + bi, where a is the real part and b is the imaginary part
The magnitude (absolute value) of a complex number z = a + bi is |z| = √(a² + b²)
The argument of a complex number is the angle it makes with the positive real axis
The complex conjugate of z = a + bi is z̄ = a - bi
Polar form represents a complex number as r∠θ, where r is magnitude and θ is argument
Rectangular form represents a complex number as a + bi coordinates
Multiplication in polar form: (r₁∠θ₁) × (r₂∠θ₂) = (r₁r₂)∠(θ₁+θ₂)
Division in polar form: (r₁∠θ₁) ÷ (r₂∠θ₂) = (r₁/r₂)∠(θ₁-θ₂)