Imaginary Numbers Definition

The number whose square results in negative results is called an Imaginary number.

In simple words, the square root of negative numbers is called an imaginary number. They are called imaginary numbers as we cannot associate them with any real-life examples.

They are represented by “i” and are pronounced as iota at its value is,

i = √-1

Examples of Imaginary Numbers

Some examples of imaginary numbers are:

. . . -3, -2i, -i, i, 2i, 3i . . .

Note:

• i is the imaginary unit, defined as i = −1​.
• ki is the positive multiple of imaginary unit, where k > 0.
• -ki is the negative multiple of imaginary units, where k > 0.

History of Imaginary Numbers

Imaginary numbers were first encountered in the 16th century as solutions to seemingly unsolvable equations. They were first encountered by Italian mathematician Gerolamo Cardano while solving cubic equations. Later, in the 18th century, the term “imaginary” was coined for these numbers by Swiss mathematician Leonhard Euler.

Initially met with skepticism, they were eventually accepted as crucial tools in solving various mathematical problems, especially in areas like electrical engineering and quantum mechanics. Imaginary numbers are represented as multiples of the imaginary unit, “i,” where i² equals -1.

Imaginary numbers are numbers as the name suggests are the number that is not real numbers. All the numbers real and imaginary come under the categories of complex numbers. Imaginary numbers are very useful in solving quadratic equations and other equations whose solutions can not easily be found using general rules.

For example, the solution of x² + x + 1 = 0 can easily be calculated using imaginary numbers. Let’s learn about Imaginary numbers and their properties in detail in this article.