\begin{definition}[Definition:Complex Modulus]
Let $z = a + i b$ be a complex number, where $a, b \in \R$.
Then 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'''.
\end{definition}