Stage 31 · Complex Numbers

31.6.3 Complex Roots Come in Pairs: Conjugate Roots

31.6 Complex Numbers and Equations: Letting Every Root Appear

Point 3 of 5

31.6.3 Complex Roots Come in Pairs: Conjugate Roots

Core idea

Picture this: the complex roots of a real-coefficient equation always arrive as a matched mirror pair; if a+bi is a root, then a−bi must be one too

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
eastmath.com · 31.6 Complex Numbers and Equations: Letting Every Root Appear · 31.6.3 Complex Roots Come in Pairs: Conjugate Roots