Complex Number Calculator
First Complex Number
Second Complex Number
Result
How to Use
- Enter the real and imaginary parts of the first complex number
- Enter the real and imaginary parts of the second complex number
- Choose an operation (Add, Subtract, Multiply, or Divide)
- View the result and step-by-step calculation
About Complex Numbers
Complex numbers are numbers in the form a + bi, where:
- a is the real part
- b is the coefficient of the imaginary part
- i is the imaginary unit (i² = -1)
Operations:
- Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
- Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
- Multiplication: (a + bi) × (c + di) = (ac - bd) + (ad + bc)i
- Division: (a + bi) ÷ (c + di) = [(ac + bd)/(c² + d²)] + [(bc - ad)/(c² + d²)]i
Common Examples
| Operation | Example | Result |
|---|---|---|
| Addition | (3 + 4i) + (1 + 2i) | 4 + 6i |
| Subtraction | (3 + 4i) - (1 + 2i) | 2 + 2i |
| Multiplication | (3 + 4i) × (1 + 2i) | -5 + 10i |
| Division | (3 + 4i) ÷ (1 + 2i) | 2.2 - 0.4i |
Applications
- Electrical engineering (AC circuits)
- Signal processing
- Quantum mechanics
- Control systems
- Fractal geometry
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