In this kind of notation, the number

*a*is called the real part and the number*b*is called the imaginary part of the complex number.The set of real numbers is a subset of the set of complex numbers. We write this as: \(\mathbb{R} ⊂ \mathbb{C}.\)

The set of imaginary numbers is a subset of the set of complex numbers.

### Examples

- The number \(\sqrt{-16}\) is a
*complex number*, because: \(\sqrt{-16}\) = 0 + 4i. - The number 25 is a
*complex number*, because: 25 = 25 + 0i.

### Historical Note

If i^{2} = −1, then: i = \(\sqrt{-1}\). and we can write: \(\sqrt{-16}\) = 0 + 4i = 0 + 4\(\sqrt{-1}\)

The symbol \(\sqrt{-1}\) appeared for the first time in the notes of Leonhard Euler (1707-1783), published in 1794.