How to Use the Complex Number Calculator
Enter z₁=a+bi and z₂=c+di, then select an operation to instantly compute the result along with the magnitude and conjugate of each complex number.
Key Formulas
- Addition: (a+c) + (b+d)i
- Multiplication: (ac−bd) + (ad+bc)i
- Division: (ac+bd)/(c²+d²) + (bc−ad)/(c²+d²)i
- Magnitude: |z| = √(a²+b²)
- Conjugate: z̄ = a−bi
Frequently Asked Questions
How is complex division performed?
Multiply both numerator and denominator by the conjugate of the denominator to make the denominator real: z₁/z₂ = z₁·z̄₂/|z₂|².
What does magnitude represent geometrically?
In the complex plane, magnitude |z| = √(a²+b²) is the distance from the origin to the point (a, b). It is also called the modulus or absolute value.
Can I use real numbers only?
Yes. Set b=0 and d=0 to compute with real numbers. The calculator handles all cases including purely imaginary (a=0) and fully complex inputs.