Imaginary Unit

What is an Imaginary Unit?

An imaginary unit in algebra is a mathematical concept denoted by the symbol i, representing the square root of -1. It is used to extend the number system to include complex numbers, which are numbers in the form a+bi, where a and b are real numbers and i is the imaginary unit.

Mathematically, $i^2=\text{-}1$ . The concept of the imaginary unit is essential in the field of complex numbers, where numbers of the form $a+bi$ include a real part $(a)$ and an imaginary part $(bi)$ .

Complex numbers allow for the representation of quantities beyond the real number line.

Imaginary Unit Explanation

$i$ is an imaginary unit, and $i^2=\text{-}1$ .
Complex numbers are written in the form $a+bi$ , where $a$ and $b$ are real numbers.
The real part of the complex number $a+bi$ is $a$ , and the imaginary part is $bi$ .
Imaginary numbers are multiples of the imaginary unit, such as $2i$ or – $3i$ .

Imaginary Unit Examples

Basic Imaginary Numbers

$i$
$2i$
– $3i$

Complex Numbers

$3+4i$
– $2-i$
– $1-2i$

Operations with Imaginary Units

$i\times i=i^2=-1$
$(3+2i)+(1-5i)=4-3i$
$(2-i)(3+2i)=6+4i-3i-2^i=8+i-2(-1)=10+i$