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Mathematics · Glossary

What is Affix, modulus?

Also known as: affix · modulus

Definition 28.6 High School Mathematics · Chapter 28 — Complex Numbers

In the plane with orthonormal coordinates, the point M(a,b)M(a, b) is the image of z=a+ibz = a + \iu b, and zz is the affix of MM. The modulus of zz is the distance from MM to the origin:

∣z∣=a2+b2=zz‾.\abs{z} = \sqrt{a^2 + b^2} = \sqrt{z\conj z}.
The point M(a,b) of affix z: the modulus z is the length OM, and the conjugate z is the reflection of z in the real axis.
The point M(a,b)M(a,b) of affix zz: the modulus ∣z∣\abs z is the length OMOM, and the conjugate z‾\conj z is the reflection of zz in the real axis.
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