# Powers of i Activity

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Yesterday, after spending a bit of time laminating and cutting out the cards for the trig open middle task I posted about yesterday, As I was looking through the Open Middle tasks for complex numbers, I got the idea of creating a task involving the powers of i (imaginary numbers). I was shocked at first that this didn’t already exist. Then, I remembered why. Oh, yes, Oklahoma had to go and get rid of Common Core and write its own standards. The Oklahoma standards require students to be able to evaluate various powers of i.

After throwing together a mock-up of the powers of i activity in Paint and realizing that it was solveable, I typed up the puzzle in Microsoft Publisher. The task of the powers of i activity is to use the digits 1-9, at most one time each, to fill in the boxes to create four true statements involving powers of i.

I also created some 1-9 cards to fit exactly in the exponent boxes of the powers of i activity. This helps ensure that students use each number at most once. Plus, I just like puzzles with moveable pieces!

A major perk of having a math teacher husband is that he is always glad to test out any of my creations.

Sadly, I was too slow to take a picture of my husband solving the puzzle. By the time I snapped my picture, he had solved the entire thing. I try my best to not post pictures of solutions here on my blog because I know that my creations are easily googleable by students!

I’m not entirely happy with this puzzle at the moment. I was able to find a solution very quickly as was my husband. But, I’m conflicted. Were we able to find solutions so quickly because the puzzle is too easy? Or are we finding solutions so quickly because we both have math degrees? How long would it take Algebra 2 or Pre-Calc students to tackle this task? I’m not entirely sure. But, I’m still looking forward to finding out.

This is not the sort of task that I would make an entire lesson out of. It’s not meaty enough for that. But, I do think that this task is perfect for a semi-quick lesson opener or closer. Or, it could be used as a station activity that students rotate between.

If you are looking to increase the challenge of the powers of i activity, I would suggest challenging students to solve the puzzle in such a way that the exponents are in increasing order as you move down the page. It’s still a very solveable puzzle, but it did require us to do quite a bit more fiddling with the numbers to make it work. If you have a group of students finish the original puzzle way too quickly, this could make a nice extension.

I’m also open to hearing constructive criticism about how to make this task better.

## Free Download of Powers of i Activity

Powers of i Activity (PDF) (1505 downloads )

Powers of i Activity (Editable Publisher File ZIP) (983 downloads )

Wow, Sarah, I am impressed at how creative and productive you are with a little one to keep track of! I understand you may not want to blog/post pictures of him, but I hope everyone is doing well!

This activity worked great in my room! We did powers of i today in class and used this as our finishing activity. We did three 'rules.' First was only use each number once. Second was increasing size of exponents. (Both of which you mentioned.)

The third rule was kind of fun. When they found a solution, they wrote the last exponent (ex. 875) in a spot on the board and then no one else could use that number in their work anymore.