Description
Return real monic quadratic coefficients for a 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 real monic quadratic coefficients for a conjugate root pair.
When to use this tool
Use Complex Linear Factor Real Part when checking the stated polynomial transformation or complex-coordinate term.
How to use the tool and how it works
- Enter rootReal, rootImaginary. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read linearCoefficient, constant. Use the output convention below.
Return real monic quadratic coefficients for a conjugate root pair. linearCoefficient = -2*rootReal, constant = rootReal²+rootImaginary².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rootReal | Root Real | Required. Finite number. |
| rootImaginary | Root Imaginary | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| linearCoefficient | Linear Coefficient | Required. Finite number. |
| constant | Constant | Required. Finite number. |
{
"input": {
"rootReal": 2,
"rootImaginary": 3
},
"output": {
"linearCoefficient": -4,
"constant": 13
}
}Limitations and assumptions
- The leading coefficient is implicitly one and the imaginary part may be signed; no actual polynomial or root validity is verified.
- 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.
- Polynomial Complex Conjugate Root Pair
Return a supplied conjugate root pair.