Not much to say here, except that you may want to reuse this extra credit on your own test—if they learn it from the sample (by asking you) and then get it right on your test, they learned something valuable.

Inside Collection: Advanced Algebra II: Teacher's Guide

Summary: A teacher's guide to the square root of the imaginary number.

This is arguably the most advanced, difficult thing we do all year. But I like it because it contains absolutely nothing they haven’t already done. It’s not here because it’s terribly important to know

Explain the problem we’re going to solve, hand it out, and let them go. Hopefully, by the end of class, they have all reached the point where they know that

Note that right after this in the workbook comes a more advanced version of the same thing, where they find

They should finish the worksheet if they haven’t done so, including #7. Then they should also do the “Homework: Quadratic Equations and Complex Numbers.” It’s a good opportunity to review quadratic equations, and to bring in something new! (It’s also a pretty short homework.)

When going over the homework, make sure they did #3 by completing the square—again, it’s just a good review, and they can see how the complex answers emerge either way you do it. #4 is back to the discriminant, of course: if

The fun is seeing if anyone got #5. The answer, of course, is that the two roots are complex conjugates of each other—real part the same, imaginary part different sign. This is obvious if you rewrite the quadratic formula like this:

and realize that the part on the left is always real, and the part on the right is where you get your

Not much to say here, except that you may want to reuse this extra credit on your own test—if they learn it from the sample (by asking you) and then get it right on your test, they learned something valuable.

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Comments:"This is the "teacher's guide" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing […]"