Welcome to our fun (and admittedly geeky) web site that is totally dedicated to imaginary numbers. Here at picomonster, we explore typical imaginary number questions such as, “Can you show me examples of imaginary numbers in the real world?” or “Are there any practical applications of imaginary numbers?”

In general, imaginary numbers are used in combination with a real number to form something called a complex number, a+bi where a is the real part (real number), and bi is the imaginary part (real number times the imaginary unit i). This complex number is useful for representing two dimensional variables where both dimensions are physically significant. Think of it as the difference between a variable for the length of a stick (one dimension only), and a variable for the size of a photograph (2 dimensions, one for length, one for width). For the photograph, we could use a complex number to describe it where the real part would quantify one dimension, and the imaginary part would quantify the other.

Don’t see the interactive applet?

You may need the Java plugin.

Install it here.

The key point to remember is that imaginary numbers are often used to represent a second physical dimension. Remember, a purely imaginary voltage in an AC circuit will shock you as badly as a real voltage – that’s proof enough of it’s physical existence!

Let’s look quickly at a fun concept – imaginary motion. Hit the “Imaginary” button in the figure left to see an engineer’s definition of Imaginary motion. Clearly, this motion is every bit as physical as “Real” motion (hit “Real” button for comparison). Imaginary doesn’t directly imply non-existent as some may believe.

But if Imaginary motion is physical, what makes it “Imaginary”?

We use some cool interactive gadgets to answer this question and more, taking you from the dry math to a solid grasp of *how* imaginary numbers are used in real world applications. Each of our three pico-lessons takes only two minutes. Have fun!

0. Home

1. Mapping Imaginary to Physical – Lesson 1

2. Complex Numbers and Dynamic Systems – Lesson 2

3. An Imaginary Number Application – Lesson 3

B. The Physical Link of the Imaginary Unit – Bonus Lesson

*PS. Thanks everybody so far for your comments. It’s been a lot of fun reading them all. *

*Bradley Chung*