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What Is the Difference Between a Real Number and An Imaginary Number?

Learn to tell the difference between real and imaginary numbers.

By
Jason Marshall, PhD
1-minute read

 

Real numbers include all rational numbers (numbers that can be written like fractions) and all irrational numbers (numbers that cannot be written like fractions). Each of the infinite number of points on the real number line represents a real number. 

Believe it or not, there are other types numbers that aren’t on the real number line. They're called "complex numbers," and they're made by adding together a real number (like the ones we know and love) and something else called an "imaginary number." 

What do imaginary numbers look like? Well, they’re sort of like real numbers, but they’re definitely stranger. We won’t go into all the details here, but imaginary numbers are all multiples of something called the imaginary unit, which we write with the letter i. And--here comes the strange part--this imaginary unit has the unusual property that its square is a negative number. In particular, i^2 = –1...which is definitely something you don’t see with real numbers!

For more, see What are Real Numbers?

 

About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.