Definition:Complex Modulus/Also known as

Complex Modulus: Also known as

The (complex) modulus is also known as the absolute value.

Others use that term only for the absolute value of a real number.

The notation $\bmod z$ is sometimes seen for $\cmod z$, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ $\cmod z$ is preferred.

It is to be noted that the term complex modulus is technically inaccurate, on the grounds that it is not the modulus itself which is complex.

However, it has been chosen for $\mathsf{Pr} \infty \mathsf{fWiki}$ for its relative ambiguity when distinguishing it from other uses of the term modulus.

Most sources prefer instead the term modulus of a complex number, which, while accurate and unambiguous, is more unwieldy and cumbersome than complex modulus.

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory: $(1.8)$
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Subgroups
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Absolute Value
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): absolute value: 2.
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms: $(3)$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): absolute value: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complex number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): absolute value: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complex number
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): modulus of a complex number (moduli)