Math
Complex number modulus
Find the distance of a complex number from the origin of the complex plane.
Calculators / Math / Complex multiplication
Complex multiplication calculator
Multiply two complex numbers entered as real and imaginary components.
On this page
Product real part-5
Product imaginary part10
Calculator controls
How to calculate
Multiply two complex numbers entered as real and imaginary components.
Product real part = a*c-b*d; Product imaginary part = a*d+b*c
Worked example
First real part: 1; First imaginary part: 2; Second real part: 3; Second imaginary part: 4.
Product real part: -5 ; Product imaginary part: 10 .
Assumptions and limits
Uses (a + bi)(c + di) with i² = −1. Read the two result components together as the product.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Multiply two complex numbers entered as real and imaginary components.
When this tool is useful
Product real part = a*c-b*d; Product imaginary part = a*d+b*c
Understanding your inputs
| Input | What to enter |
|---|---|
| First real part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| First imaginary part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Second real part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Second imaginary part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Uses (a + bi)(c + di) with i² = −1. Read the two result components together as the product.
How is the result calculated?
Product real part = a*c-b*d; Product imaginary part = a*d+b*c