Symbols:C

Hexadecimal

$\mathrm C$ or $\mathrm c$

The hexadecimal digit $12$.

The $\LaTeX$ code for $\mathrm C$ or $\mathrm c$ is \mathrm C or \mathrm c.

The Set of Complex Numbers

$\C$

The set of complex numbers.

The $\LaTeX$ code for $\C$ is \mathbb C or \C.

The Set of Non-Zero Complex Numbers

$\C^*$

The set of non-zero complex numbers:

$\C^* = \C - \left\{{0}\right\}$

The $\LaTeX$ code for $\C^*$ is \mathbb C^* or \C^*.

Relative Complement

$\complement_S \left({T}\right)$ or $\mathcal C_S \left({T}\right)$

Let $S$ be a set , and let $T \subseteq S$, that is: let $T$ be a subset of $S$.

Then the set difference $S \setminus T$ can be written $\complement_S \left({T}\right)$, and is called the relative complement of $T$ in $S$, or the complement of $T$ relative to $S$.

Thus:

$\complement_S \left({T}\right) = \left\{{x \in S : x \notin T}\right\}$

The $\LaTeX$ code for $\complement_S \left({T}\right)$ is \complement_S \left({T}\right).

The $\LaTeX$ code for $\mathcal C_S \left({T}\right)$ is \mathcal C_S \left({T}\right).

Set Complement

$\complement \left ({S}\right)$ or $\mathcal C \left ({S}\right)$

The set complement (or, when the context is established, just complement) of a set $S$ in a universe $\mathbb U$ is defined as:

$\complement \left ({S}\right) = \complement_\mathbb U \left ({S}\right) = \mathbb U \setminus S$

See the definition of Relative Complement for the definition of $\complement_\mathbb U \left ({S}\right)$.

The $\LaTeX$ code for $\complement \left ({S}\right)$ is \complement \left ({S}\right).

The $\LaTeX$ code for $\mathcal C \left ({S}\right)$ is \mathcal C \left ({S}\right).