🔢 Imaginary Number Calculator
Perform operations with complex numbers (a + bi)
Complex Number A
A = 3 + 4i
Complex Number B
B = 1 + 2i
Operation
Complex Number Basics
Key Concepts
- i² = -1 (definition of i)
- i³ = -i
- i⁴ = 1
- Conjugate of (a + bi) = (a - bi)
- |a + bi| = √(a² + b²)
Operations
- Addition: Add real and imaginary parts separately
- Multiplication: Use FOIL, replace i² with -1
- Division: Multiply by conjugate of denominator
- Polar form: z = r(cos θ + i sin θ)
About Imaginary Number Calculator - Complex Number Operations
Calculate with imaginary and complex numbers. Add, subtract, multiply, divide, and convert to polar form easily.
Our **Imaginary Number Calculator** simplifies complex number arithmetic by handling calculations involving the imaginary unit *i* (where i² = -1). Whether you need to add, subtract, multiply, or divide complex numbers, this tool provides step-by-step solutions. For related math operations, explore our Complex Number Calculator.
Complex numbers have the form a + bi, where 'a' is the real part and 'b' is the imaginary part. They're essential in electrical engineering, quantum physics, signal processing, and advanced mathematics. Convert between rectangular and polar forms for circuit analysis. Try our Logarithm Calculator for more advanced math.
Understanding imaginary numbers opens doors to solving equations that have no real solutions, analyzing AC circuits, and working with wave functions. Our calculator provides magnitude, argument (phase angle), and conjugate calculations automatically. For calculus applications, see our Tangent Line Calculator.
Key Features
Why Use This Tool?
Common Use Cases
Electrical Engineering: Analyze AC circuits and impedance.
Physics: Solve quantum mechanics problems.
Mathematics: Find roots of polynomials with no real solutions.
Signal Processing: Work with Fourier transforms.
Related Tools
How to Use
Enter the real and imaginary parts of first number
Enter real and imaginary parts of second number
Select the operation (add/subtract/multiply/divide)
Click Calculate
View result with steps and polar form