# That's Complex!

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## Objective

SWBAT explain the basic form of complex numbers.

#### Big Idea

Introduce your students to complex numbers by letting them be active problem solvers.

## Set the Stage

10 minutes

I begin this lesson with a simple quadratic on the board (like x^2-2x+4) that doesn't factor easily.  I challenge my students to find the zeros and walk around listening while they work on it. (MP1) I expect at least a few will try to find them by graphing, to no avail while others will try to factor, again with limited success.  I hope that a few remember the quadratic formula, but if not, I refresh their memories.  This will result in an answer, (1+- sqrt of -3) but I don't let my students rest there. I ask them "How can you have a sqrt of -3?  What does it mean?!"  This has resulted in all sorts of interesting explanations in previous classes, but my favorite so far was the student who said "It doesn't have to mean anything, it's just math."  After a few moments of discussion I tell my students that I want to introduce them to a new player on their math team - enter imaginary numbers.  I explain that mathmaticians created "i" to represent sqrt of -1 so they could talk about things like factors of (x^2-2x+4).  I share the definition of a complex number and show the format for writing them (a + bi).

40 minutes