What this calculator does
Complex number arithmetic works out add, subtract, multiply or divide two complex numbers, plus modulus and argument. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formula(a+bi)±(c+di) = (a±c)+(b±d)i; (a+bi)(c+di) = (ac−bd)+(ad+bc)i; (a+bi)/(c+di) = [(ac+bd)+(bc−ad)i]/(c²+d²)
The inputs explained
| Field | What to enter |
|---|---|
| a (real part 1) | A number. Starts at 3. |
| b (imaginary part 1) | A number. Starts at 2. |
| Operation | Choose from Add, Subtract, Multiply, Divide. |
| c (real part 2) | A number. Starts at 1. |
| d (imaginary part 2) | A number. Starts at -4. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with a (real part 1)
Every other input is held at the calculator’s starting values while a (real part 1) varies. Select any row to load that scenario into the calculator.