## Monday, December 04, 2006

### Next Lesson: Operations on Complex Numbers

Tomorrow, the Do Now will introduce the idea of finding the distance to the origin on a coordinate plane by creating a right triangle and using the Pythagorean Theorem. Students must calculate the shortest distance from a given point back to the origin, where they left their sweeties, and therefore want to hurry back to.

Following this, I will do direct instruction on addition, subtraction, multiplication, and division. Multiplying by the complex conjugate for division will be a nice follow up to simplifying fractions like 2/(3 + root2) from the previous lessons. Then, we will recall what was learned during the Do Now to understand how to calculate the absolute value of a complex number. Students will plot complex numbers in the complex plane, and then draw a right triangle and calculate the length of the hypotenuse. I will ask students to figure out other complex numbers that have an equal absolute value, and to determine, given a set of complex numbers, which one is farthest from the origin.

Finally, students will have about 20 minutes to work on these types of problems in pairs and ask for help. Not a very exciting lesson, to be sure, but, for some reason, complex numbers and their operations seem to be hit pretty heavily on the STAR test, so it needs a lot of class time. I don't think students will be asked to find the absolute value of a complex number, but it is good scaffolding for the distance formula, which is an indispensable tool in any high school mathematician's bag of tricks.

The lesson will be posted on ILoveMath.