Definition:Complex Modulus

Definition
Let $z = a + i b$ be a complex number, where $a, b \in \R$.

The (complex) modulus of $z$ is written $\cmod z$, and is defined as the square root of the sum of the squares of the real and imaginary parts:


 * $\cmod z := \sqrt {a^2 + b^2}$

The (complex) modulus is a real-valued function, and, as and when appropriate, can be referred to as the (complex) modulus function.

Also see

 * Complex Modulus is Norm, showing that the modulus defines a norm on the field of complex numbers.
 * Modulus in Terms of Conjugate

Special cases

 * Definition:Absolute Value of Real Number, as shown at Complex Modulus of Real Number equals Absolute Value