# Complex Number

## Complex Number

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