The complex conjugate root theorem states that if a polynomial in one variable has real coefficients, and a complex number a + bi is one of its roots, then the complex conjugate a - bi is also a root of the same polynomial. The theorem holds specifically for polynomials with real coefficients, and it shows that their non-real roots always occur in conjugate pairs.
Facts
Statementif P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b being real numbers, then its complex conjugate a - bi is also a root of P. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Complex conjugate root theorem - Wikipedia
Lead sectionQuote, Lead section
if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b being real numbers, then its complex conjugate a - bi is also a root of P.
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