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
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Source Complex conjugate root theorem - Wikipedia
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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