Stage 31 · Complex Numbers

31.6.2 Complex Roots of Real-Coefficient Equations

31.6 Complex Numbers and Equations: Letting Every Root Appear

Point 2 of 5

31.6.2 Complex Roots of Real-Coefficient Equations

Core idea

Picture this: rewrite √(negative) as i√(positive) and a quadratic always yields a pair of complex roots, x=(−b±i√(−Δ))/(2a)

Module goal. We use complex numbers to complete the roots of real-coefficient equations, reclaiming what a negative discriminant used to cost us, and paving the way for counting and polynomials ahead

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