> From: Geoff Hagopian <email@example.com> > Joshua, (and MB) > > Well, (at the risk of wandering into TI-CALC list topics and > offending MB&CO - hey, the '85 is fair game for the ap test, right?) > Just like with roots of reals, it returns only the principal root: that > is, entering <sqrt>(0,1) for the principle root of the imaginary unit > returns (.707, .707). Likewise, log(-1) returns (0,1.36), while ln(-1) > returns (0,3.14).
Of course, the 86 is an 85 with tables and much more.
> Which raises the question, how much are ap students expected to know > about complex arithmetic?
Zero. It's real analysis.
> Is it fair game to ask for simplified radical > form of complex roots of a quadratic, cubic or quartic polynomial - or
> is that the trivial business of precalculus which these seniors are way > past?
It's not trivial, nor are they past it. Complex analysis awaits the hardy in the wings.
> I like to have my precalc students explore basins of attraction > using the Babylonian algorithm for polynomial roots in the complex > plane. I suppose ap students are too busy with chain rule problems to > bother with such old-hatiness...
Dave Slomer AP Calculus and Computer Science Teacher Winton Woods HS, Cincinnati, OH 45240