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Complex Number Calculator
Calculate exact Cartesian complex sums, differences, products, quotients and conjugates with rational components.
Integer or numerator/denominator component fields
Complete exact JSON report
Browser only
Runs locally in your browser. Your files, pasted content and generated output are not uploaded. Reset clears this tool’s working data.
This tool needs JavaScript. If it does not load, refresh the page and try again.
How to use this tool
- Choose Operation. Enter A real component and A imaginary component as integers or fractions.
- For arithmetic with B, enter B real component and B imaginary component; conjugation ignores both B fields.
- Select Calculate complex result and download complex-number.json.
Examples
Multiplying (1/2 - 2/3 i) by (-3/4 + 5/6 i) gives 13/72 + 11/12 i, with result squared magnitude 4525/5184.
Limitations
- At most 100 digits per integer, 256 raw UTF-16 units per selected component and 4 KiB selected input; 4,096-digit arithmetic budget, 64 KiB JSON report and 30-second processing limit.
- Denominator signs normalize; outer whitespace is allowed. Internal whitespace, decimal/scientific component syntax and a zero divisor reject.
- No polar angles, complex roots, symbolic variables.
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