Categories Help, if you don’t mind!

I’d like to flesh out our collection of complex numbers mistakes. If you’re teaching this topic in the next few months, could you send me some pictures of mistakes? I’m looking for all sorts of mistakes — either common or uncommon errors.

In the meantime, would you take a second and comment about a complex numbers mistake that you’re used to seeing from your students?

When you’re done with that, check out some of the new mistakes that I just posted…

Thanks for all the great mistakes and comments lately, guys. Keep up the great work!

1 = sqrt((-1)*(-1)) = sqrt(-1)*sqrt(-1) = i*i = -1

Not really a mistake, but rather just something to ponder. Jaysays:

I am pretty sure this is a question about a question about the primary square root, which is defined as such to prevent this confusion. Since the square root is a function, it can only have one result. The question you’re pondering is solving the equation x^2=1 vs. the function of y= sqrt(1). To get even more complex (HA!), consider 1 as the complex number (1+0i) = 1e^(0i) in Euler form. Thus the square root of 1 can be written as

(1+0i)^(1/2) = [1e^(0i)]^(1/2)
= ^(1/2) e^[(0i)(1/2)]
= 1^(1/2)e^0
= 1^(1/2)
= 1 Shelleysays:

Last year about 10 of my students treated all complex number problems on our quiz as if they were a binomial times a binomial, so Juliesays: