Introduction to Imaginary Numbers

The topic of imaginary numbers is one of the most abstract and therefore difficult math topics to teach in algebra. Here is how I introduce it to students (emphasis that this is only an introduction).

0110190730_2 (1)

I write 1, 2, 3… on the board (see photo above) and explain to the student “at some point in life you learned to count on your fingers, 1, 2, 3…” These are called the Natural numbers.

toddler counting

Then I explain, “later you were told that no cookies means ZERO cookies. Zero is a new type of number. We call 0, 1, 2, 3… the Whole numbers. You learned a new type of number.”

This continues, “A little later on you were told you could have half a cookie and so you learned about a new type of numbers called fractions.”

This continues with negatives. Then I explain that all these number types can be found on the number line. We call the set of all of these numbers Real Numbers.

I conclude with “Now we have a new type of numbers that are not found on the number line. These are called imaginary numbers. Just like before you had number types you had before and now you have a new one to learn.”

The point of this approach is to help the students understand that a new number set simply builds on previous number sets. Also, the students have encountered this situation before.

Tagged , , , , ,

3 thoughts on “Introduction to Imaginary Numbers

  1. koloradokyd says:

    One might extend the progression by noting that while real numbers are found on the real number line, imaginary numbers are found on the complex plane.

Leave a Reply to ctspedmathdude Cancel reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: