imaginary Numbers/generated numbers will multiple choice

JustinDavidson

Going over powers of i. The only answers are i, -1, -i, or 1.

First attempt was to use a formula question with i^`a` and have it randomly generate natural numbers for a. I learned that Canvas doesn't like imaginary numbers, so only will generate a values that produce 1 or -1. Not very helpful for the concept.

Multiple choice questions, to my knowledge, cannot have generated numbers/formulas in them. I'm hoping to NOT have to create a bunch of MC questions where I just change the exponent. Any ideas? TIA!

James

@JustinDavidson 

I've had to hack Canvas in similar ways before so that I can use a formula question.

What I would do is give them an answer key as part of the question.

Here is the HTML of the question. Nothing fancy other than adding extra spacing after the question prompt because Canvas doesn't.

 

<p style="padding-bottom: 1em;">Simplify \(i^{`n`}\).</p>
<p>Use these directions for entering your answer.</p>
<ul>
    <li>Enter 1 if the answer is \(1\)</li>
    <li>Enter -1 if the answer is \(-1\)</li>
    <li>Enter 2 if the answer is \(i\)</li>
    <li>Enter -2 if the answer is \(-i\)</li>
</ul>

 

We know the answer is dependent upon n mod 4. I took the easy way out and used the modulus to get the value in a specific position within a list.

• For n mod 4 = 0, we get \(i^0=1\) so we want the answer to be 1
• For n mod 4 = 1, we get \(i^1=i\) so we want the answer to be 2
• For n mod 4 = 2, we get \(i^2=-1\) so we want the answer to be -1
• For n mod 4 = 3, we get \(i^3=-i\) so we want the answer to be -2

Canvas doesn't have a facility for entering a list directly. You can use reverse() to enter it in reverse order or sort() to a list. Sort() won't help, but reverse() will maintain the order. Since we want 1, 2, -1, -2, we have to enter it as reverse(-2, -1, 2, 1).

Once you have a list, you can use the at() function to get the number from a certain position. It uses a 0-based index, which works great with our remainders.

Here's the code I used for the answers.

 

at(reverse(-2,-1,2,1),mod(n,4))

 

Using this technique allows you to change the codes. For example, you could say enter 1, 2, 3, or 4. The reason I went with the weird way I did is that it's going to be confusing to the student to enter 3 when the answer is -1, but they can see that the i thing is different.

You might add a note that the reason we're using the conversion table is because Canvas will not allow you to enter an i with a formula question.