Description
Return a supplied conjugate root pair.
Polynomial transformations change coefficient scales or root coordinates under an explicit substitution. Translation, reflection and dilation use different signs, while a single complex phase does not apply a complete root-of-unity filter. The original function’s domain still matters after rational cancellation.
Return a supplied conjugate root pair.
When to use this tool
Use Polynomial Complex Conjugate Root Pair when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter realPart, imaginaryPart. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read realParts, imaginaryParts. Use the output convention below.
Return a supplied conjugate root pair. Require imaginaryPart >= 0; realParts repeats realPart, imaginaryParts returns positive/negative magnitude, using two zeros when magnitude is zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| realPart | Real Part | Required. Finite number. |
| imaginaryPart | Imaginary Part | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| realParts | Real Parts | Required. Array of finite number; maximum items 256. |
| imaginaryParts | Imaginary Parts | Required. Array of finite number; maximum items 256. |
{
"input": {
"realPart": 2,
"imaginaryPart": 3
},
"output": {
"realParts": [
2,
2
],
"imaginaryParts": [
3,
-3
]
}
}Limitations and assumptions
- No polynomial is derived or solved; real coefficients, root identity and multiplicity are supplied assumptions.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the full transformed expression and explicit variable substitution for complete symbolic equivalence, filtering or root analysis.
References
Similar or alternative tools
- Complex Conjugate Root Factor Coefficients
Return ascending monic quadratic coefficients for a supplied conjugate pair.
- Cubic Root Unity Filter Term
Return one cube-root-of-unity phase power.