A non-real number is a type of number that cannot be found on the standard number line, which includes rational and irrational numbers. The most common examples of non-real numbers are complex numbers, specifically those that have an imaginary component.
To understand this, we have to look at the concept of imaginary numbers. Imaginary numbers are multiples of the imaginary unit ‘i’, which is defined as the square root of -1. Therefore, when we encounter equations that require taking the square root of a negative number, the solutions to those equations result in non-real numbers. For instance, the square root of -4 is represented as 2i.
Non-real numbers play a crucial role in various fields of mathematics and engineering, as they help solve problems that cannot be addressed using only real numbers. They are particularly important in complex number theory, electrical engineering, and quantum physics.