Complex Numbers Calculator
Calculate sum, difference, products, and quotients of complex values ($a + bi$) with real-time vector graphs.
Enter Complex Numbers
Complex Plane Vectors
4 + 2i
Step-by-Step Derivation:
What is the Complex Numbers Calculator?
The Complex Numbers Calculator handles arithmetic operations (addition, subtraction, multiplication, division) involving imaginary numbers. Complex numbers are crucial in advanced calculus, quantum physics, and AC circuit analysis in electrical engineering.
How It Works (Formula)
A complex number takes the form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part (with \(i\) being the square root of -1). When performing operations, the calculator algebraically isolates and combines the real components and the imaginary components separately.
$$ (a + bi) + (c + di) = (a+c) + (b+d)i $$
The fundamental rule of complex addition: group real and imaginary terms.
How to Use It
Enter the real and imaginary components of your first complex number. Select the mathematical operator (+, -, *, /) and enter your second complex number. The tool will output the fully resolved final complex number.