Question

What does the symbol $C$ signifies?

Answer 1

Here we are asked the significance of symbol in Mathematics. So we need to write its meaning, relevance and applications.

Complete step-by-step answer:
In Mathematics we use certain notations for expressing information. We use capital letters $A,B,C...$ for denoting sets and small letters for elements in the sets.
But there are some fixed notations for peculiar or commonly used sets such as natural numbers, integers, real numbers, complex numbers etc.
The letter $C$ is generally used to denote the set of complex numbers.
A complex number is a number that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers and $i$ represents the imaginary unit, satisfying the equation ${i^2} = - 1$. For a number of the form $a + bi$, $a$ is called the real part and $b$ is called the imaginary part.
Complex numbers can be represented in a plane in the form of ordered pair $(a,b)$.

Additional information:
Like sets of complex numbers is denoted by $C$, we have other standard notations also.
$N$ is used to denote the set of natural numbers.
$W$ is used to denote the set of whole numbers.
${\rm Z}$ is used to denote the set of integers.
$R$ is used to denote the set of real numbers.

Note: The letter $C$ is used for different notations in different aspects. Here we are discussing the significance in Mathematics only. Also it can be used to denote a random set other than complex numbers as well if mentioned specifically.