The set of complex numbers, represented by the symbol $\mathbb{C},$ is formed by all numbers that can be written in the form $z=a+bi,$ where $a$ and $b$ are real numbers, and $i$ is the imaginary unit. Here, $a$ is called the real part and $b$ is called the imaginary part of the complex number.

If $b\neq 0,$ the number is an imaginary number. Conversely, if $b=0,$ the number is real. Both real numbers and imaginary numbers are subsets of the complex number set.