# Common Core Standards: Math See All Teacher Resources

#### The Standards

# High School: Number and Quantity

### The Complex Number System HSN-CN.A.1

**1. Know there is a complex number i such that i^{2} = -1, and every complex number as the form a + bi with a and b real.**

It's a little-known fact that in Disney World, in the Journey into the Imagination Pavilion, lives a purple dragon named Figment. (No, Figment is not Barney. They're not even related. Figment is a *dragon*, not a dinosaur, and he doesn't have that annoying voice or theme song.) Figment is quite a rule breaker—he does things that others tell him he simply can't.

Before the ride was rehabbed, there was a wall toward the end of the ride. It pictured all sorts of things imaginary—pigs that flew and three headed cows and the expression "*i*^{2}= -1."

What on Earth are we talking about? Well, what the Imagineers at Disney remembered from high school is that there is a field of numbers based on something imaginary. We call this field of numbers "complex numbers" (since "imaginary" sounds a tad too mythical) and its most basic unit is the number *i*. Yes, the number. Not the letter.

What's the big deal about *i*? Well, the big deal is that *i* = .

Yeah, we know. Square roots and negative numbers just don't go together. Well that was then, and this is now.

Once your students get past the idea that -1 can have a square root, they can have lots of fun with imaginary numbers. The complex number system is composed of numbers in the form "*a* + *bi*," where both *a* and *b* are real numbers. (That means we can have numbers like 2 + 5*i* or 7 – 12*i*.) Eventually, they can even do all sorts of operations with complex numbers.

We'll take it one step at a time, though.