PREP 2014 Question Authoring - Archived

Conjectures? with complex variables?

Conjectures? with complex variables?

by Murphy Waggoner -
Number of replies: 0
A common activity for me to assign to students is to collect some data through calculations, make conjectures about those calculations, and then prove or disprove the conjectures.

It seems that I should be able to automate the first two parts of this activity on WebWork as long as it is fairly obvious what the conjecture should be. The students would know that their data is correct, which is a bonus instead of trying to make a conjecture based on incorrect data. I'll ask for proofs of the conjectures in some other fashion.

However...a conjecture in the form of an equation may be written in many different ways, and so we get back to ImplicitEquation. This would be fine in a real variable class, but I'm writing questions for Complex Variables.

Other than simply asking for the conjecture in an essay question for me to have to grade later, any suggestions that would not lead the student too much (such as Re z = __________. Ick.)

I would include the WW problem here, but it is routine: Calculate the following, with the usual answer checking, and then an essay question whether they enter their conjecture.

I have them calculate z + conj(z), Re z, Im z, | z | for 4 random complex numbers, none are the same and for each the real and complex parts are not the same and not negatives of each other. Then I am hoping they can conjecture that z + conj(z) = 2Re z .