How to use the complex number multiplication calculator
Multiply two complex numbers. Enter real a, imag b, real c, imag d in the fields above; the real part, imaginary part, modulus are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “multiply a+bi”, “product of complex numbers”, “imaginary arithmetic”, “calculate complex number multiplication”, “find real part”.
Formula
Variables
- a — Real a
- b — Imag b
- c — Real c
- d — Imag d
Worked example
With real a = 2, imag b = 3, real c = 1, imag d = -4, the calculator gives real part ≈ 14; imaginary part ≈ -5; modulus ≈ 14.86607.
Frequently asked questions
What is the complex number multiplication calculator used for?
Multiply two complex numbers. It helps with questions such as “multiply a+bi”, “product of complex numbers”, “imaginary arithmetic”.
What is the formula for the complex number multiplication calculation?
Real part = a × c-b × d. Imaginary part = a × d+b × c. Modulus = hypot([Real part],[Imaginary part]). Here a is real a, b is imag b, c is real c, d is imag d.
What inputs do I need for the complex number multiplication calculator?
You need real a, imag b, real c, imag d. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the complex number multiplication calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the complex number multiplication result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.