How to use the complex conjugate calculator
Prepare the values for this calculation
Calculate the complex conjugate of a+bi. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Real part: enter a finite number. Use the unit named in the label or selected above. Do not leave this required field blank.
- Imaginary part: enter a finite number. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Complex conjugate first. With the unchanged example inputs, it is 3 - 4i. Interpret it using the formula and assumptions on this page.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Real part from 3 to 3.3. The resulting Complex conjugate is 3.3 - 4i. This illustrates the equation’s response to that input, rather than a forecast of real events.
The result diagram shows the inputs, method and output. A numeric chart is shown only when the calculation supports a meaningful numeric relationship.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Complex Conjugate Calculator formula
conj(a+bi) = a−bi.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Real part | Number | 3 |
| Imaginary part | Number | 4 |
Worked example
Using the example inputs above, the complex conjugate is 3 - 4i.
- Complex conjugate
- 3 - 4i
Results and assumptions
The output uses the complex conjugate convention and formula shown above. Match the entered units and source assumptions when comparing results.
Fix an input or unexpected result
Real part is required. Enter real part using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.