Comments on: Journey into Complex Numbers http://teachingcollegemath.com/2009/01/journey-into-complex-numbers/?utm_source=rss&utm_medium=rss&utm_campaign=journey-into-complex-numbers Thu, 02 Feb 2012 19:57:32 +0000 hourly 1 http://wordpress.org/?v=3.3 By: sam shah http://teachingcollegemath.com/2009/01/journey-into-complex-numbers/comment-page-1/#comment-470 sam shah Thu, 08 Jan 2009 02:01:00 +0000 http://teachingcollegemath.com/?p=504#comment-470 howdy! I actually used that in class yesterday. I had three students with paper copies, and I projected it for the rest of the class to see. One student was John, one student was Betty, and the most histrionic student was chosen to be the Narrator. <br/><br/>When John and Betty figured out how to add complex numbers, or multiply, or divide, I would explain and then have students work out 4-6 problems to check their understanding.<br/><br/>And the building up from integers to fractions to irrational numbers (well, algebraic numbers technically) was perfect, because when someone said "i doesn't exist", I could ask them if sqrt(3) existed... and that discussion really helped.<br/><br/>This year it went so much smoother than last year.<br/><br/>I also didn't even talk about sqrt(-1) in the class. I only spoke of a number, when multiplied by itself, which gave -1. (Like in John and Betty.) I think that was crucial, because when you introduce the idea that i=sqrt(-1), you then have to have the discussion why i*i=sqrt(-1)*sqrt(-1)=sqrt(-1*-1)=sqrt(1)=1 doesn't work. Which complicated things for them from the outset last year.<br/><br/>Sam<br/><br/>I howdy! I actually used that in class yesterday. I had three students with paper copies, and I projected it for the rest of the class to see. One student was John, one student was Betty, and the most histrionic student was chosen to be the Narrator.

When John and Betty figured out how to add complex numbers, or multiply, or divide, I would explain and then have students work out 4-6 problems to check their understanding.

And the building up from integers to fractions to irrational numbers (well, algebraic numbers technically) was perfect, because when someone said “i doesn’t exist”, I could ask them if sqrt(3) existed… and that discussion really helped.

This year it went so much smoother than last year.

I also didn’t even talk about sqrt(-1) in the class. I only spoke of a number, when multiplied by itself, which gave -1. (Like in John and Betty.) I think that was crucial, because when you introduce the idea that i=sqrt(-1), you then have to have the discussion why i*i=sqrt(-1)*sqrt(-1)=sqrt(-1*-1)=sqrt(1)=1 doesn’t work. Which complicated things for them from the outset last year.

Sam

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