Concept

The Imaginary Unit

The imaginary unit

i

- 1,

that is,

i = - 1 .

From this definition, it can also be said that

i^{2} = - 1 .

Imaginary Unit
$i = - 1$ or $i^{2} = - 1$

The imaginary unit

i

can also be regarded as a solution to the equation

x^{2} + 1 = 0 .

x^{2} + 1 = 0 \Rightarrow i^{2} + 1 = 0

The imaginary unit allows to rewrite the square root of any negative number. Once

i

replaces the square root of

- 1,

the square root of the remaining positive number can be evaluated as usual.

$- a = a \cdot - 1 = a \cdot i$

The above property is true only when

a > 0 .

Here are some examples of how to use the property to simplify radical expressions.

- 5 - 4 - 20 = 5 \cdot i = 4 \cdot i = 2 i = 20 \cdot i = 4 \cdot 5 \cdot i = 25 \cdot i

The combination of real numbers and any expression of the form

b i,

with

b \neq = 0,

creates a new set of numbers called imaginary numbers.