Tag Archives: complex numbers

Precal Files: Polar Coordinates and Complex Numbers

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A quick aside before I start sharing: in one of our tours in Iceland, the tour guide mentioned that 3 Miss Worlds have come from Iceland.  Since there’s about 320,000 citizens, and about half of those are female, it means that you have a 1 in 50,000 chance of meeting a Miss World in one of the bars (there was also a side note about the Vikings choosing all the pretty women from Ireland and Scotland to take and leaving them with….). Then the punchline: “Iceland: where everyone is statistically exceptional.” How could I not like this country? Plus over half the population does not discount the fact that there could be elves. Oh, and they eat ice cream all the time.

One thing they do not have in Iceland is polar bears. But if they did, wouldn’t that be an awesome segue into polar coordinates?

Alas, I guess we’ll just have to start with some Polar Coordinate Battleship then these notes:

Files from megcraig.orgFile here.

And some equations, and a hint of graphing by hand:

Files from megcraig.orgFiles from megcraig.orgFile here.

The first year I did polar equations, we just did them all by hand and did some noticing. If you’d also like to, here’s a worksheet:

Files from megcraig.orgFile here.

This year, I did a desmos exploration (read more about it here):

Files from megcraig.org

Files from megcraig.orgFiles from megcraig.orgFile here and desmos file here.

Sadly, the title is cut off of the next worksheet, it’s labeled as “The Greatest Polar Graph NoteTakerMaker Ever.”

Files from megcraig.org

Does the fact that a negative rotates a lemniscate 90 degrees make you freak out because HOLY CRAP THAT’S WHAT IMAGINARY NUMBERS DO ON A NUMBER LINE WHAT THE HELL, MATH??? or is that just me?

File here.

We did some practice with matching (from Mastermathmentor) and some practice sketching worksheets (from another teacher).  Also a wee bit of “where do two polar graphs intersect?” I’d also point you to Michael’s Reason and Wonder polar posts for some more ideas on introducing and graphing.

Then some complex numbers:

Files from megcraig.orgFiles from megcraig.orgFile here.  I did a lot of stuff in class (this actually took us two days) from the Better Explained website: here, here, and here.

Finally a study guide:

Files from megcraig.orgFile here. And study guide videos: #1-16, #17-26, and #27-37 (even though it says 17 as the first problem-doh!)

Find more precal files and FAQs here. Hope you’re finding these helpful! 🙂