Yesterday was the first day of the semester. Time to figure out how to teach again. I met my first class. They seem like great kids. We also had a Math/Science department adjunct meeting. Things went real well. Paul Argazzi even gave me three new problems. These are fun.

Simplify

Factor

Evaluate

Let the fun begin!

## Saturday, January 24, 2009

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## 2 comments:

I was wondering if anybody can further simplify what I come up with for the middle problem.

(x^2-5/2+(3/2)i)(x^2-5/2-(3/2)i)

The first problem works out to

-5+2i or 5-2i

and the last is, naturally,

log cabin

The middle problem intrigued me so much I continued to work on it by factoring my two quadratics. This gave me four factors. I ended up making a calculation error (I later learned) so I won't include them here. It seemed to me I must be missing something though because my result was pretty complex (pun unintentional but I'll take it).

So, I asked Paul for some help. He gave me his solution and it is really cool.

If you would like to see if you can find it yourself, here's a hint: add and subtract an x^2 term in the original expression so you end of with the difference of two squares.

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