What is the Difference Between Real Numbers and Imaginary Numbers?

The main difference between real numbers and imaginary numbers lies in their properties and applications. Here are the key differences:

• Real Numbers: These are numbers that can be expressed as natural numbers, whole numbers, integers, rational numbers, or irrational numbers. Real numbers are represented by the "R" symbol. They can be either positive or negative, and they are used in various applications in the real world, such as measurements, counting, and calculations in fields like aviation, electronics, and engineering.
• Imaginary Numbers: These are numbers that are the product of a real number and "i," where "i" is the imaginary unit defined as √(-1). Imaginary numbers are used to evaluate the square root of negative numbers, such as √(-9) = √(-1) * 3 = 3i. The square of an imaginary number is always negative, and they are often used in complex numbers, which are the sum of a real and an imaginary number.

In summary, real numbers are numbers that can be expressed in various forms and are used in a wide range of applications, while imaginary numbers are used to evaluate the square root of negative numbers and are often used as part of complex numbers. Both real and imaginary numbers are subsets of complex numbers, which are the sum of a real and an imaginary number.

Comparative Table: Real Numbers vs Imaginary Numbers

Here is a table comparing the difference between real numbers and imaginary numbers:

Real numbers include all the familiar number types, such as natural, whole, integer, rational, and irrational numbers. Imaginary numbers, on the other hand, are the product of a real number and "i", where "i" is the square root of -1. Real numbers can be plotted on a number line, while imaginary numbers cannot be plotted on a number line.