Stage 31 · Complex Numbers

31.4.2 Conjugate Meets Modulus: z·z̄=|z|²

31.4 Conjugate and Modulus: a Pair of Mirror Images at Work

Point 2 of 4

31.4.2 Conjugate Meets Modulus: z·z̄=|z|²

Core idea

Picture this: multiply a number by its own mirror image and the imaginary parts cancel out perfectly, leaving a real number that equals exactly the modulus squared

Module goal. We get a systematic feel for the conjugate and how it relates to the modulus, treating it as a central tool for working with complex numbers
eastmath.com · 31.4 Conjugate and Modulus: a Pair of Mirror Images at Work · 31.4.2 Conjugate Meets Modulus: z·z̄=|z|²