Number that can be written in the form a + bi where a and b are real numbers
and i2 = −1.
and i2 = −1.
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 i2 = −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.