How it works
Use componentwise addition/subtraction, (a+bi)(c+di)=(ac−bd)+(ad+bc)i, and multiply by the divisor’s conjugate for division.
Input definitions
- First real component
- Enter the value in the labeled unit.
- First imaginary component
- Enter the value in the labeled unit.
- Second real component
- Enter the value in the labeled unit.
- Second imaginary component
- Enter the value in the labeled unit.
- Operation
- Choose Multiply / Add / Subtract / Divide.
A worked example
- First real component
- 2
- First imaginary component
- 3
- Second real component
- 4
- Second imaginary component
- -1
- Operation
- Multiply
Assumptions & limits
Finite numeric components, rounded to six decimal places in the formatted answer. No symbolic radicals or arbitrary precision.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Can I divide by a purely imaginary number?
Yes, provided its magnitude is nonzero and numerically representable. Division uses the complex conjugate so both real and imaginary parts are handled.
How does Complex number arithmetic work?
Use componentwise addition/subtraction, (a+bi)(c+di)=(ac−bd)+(ad+bc)i, and multiply by the divisor’s conjugate for division.
What are the limits of Complex number arithmetic?
Finite numeric components, rounded to six decimal places in the formatted answer. No symbolic radicals or arbitrary precision.