A complex number is part of the set of complex numbers which we represent as the symbol, $\mathbb{C}$. Thus any complex number is part of this set $\mathbb{C}$. Suppose we have complex number, $z$.

Now since its a complex number we can say that, $z$ is part of the set of complex numbers, $\mathbb{C}$, which we write as $z \in \mathbb{C}$

Now the general formula for our complex number, or any complex number, can be written as:

$z=a+b i$

where

$a$ and $b$ are real numbers i.e. $a$ and $b$ in the set of real numbers, $\mathbb{R}$, which we can again write as $a, b \in \mathbb{R}$

The complex number is made up of two parts. They are:

- The real part, which is $a$ (We can show this as $\operatorname{Re}(z)=a$ )
- The imaginary part, the number in front of the $i$, which is $b$ (We can show this as $\operatorname{Im}(z)=b$ )

(because its like how we show real numbers on the Cartesian plane $(x, y))$