principal value – BAD MATHEMATICS

UPDATE (29/08/21)

Sigh. We really hate updating WitCHes.* We have about a hundred of these things to do, and we’re generally thinking of the updating as a task for retirement or, better, for a reincarnation. However these NHT WitCHes, and this one in particular, have highlighted a degree of confusion. So, alas, it seems worthwhile sorting out the issues while the issues are in mind.

We’re amazed we didn’t know about this one, which was brought to our attention by commenter P.N.. It comes from the 2013 Specialist Mathematics Exam 2:

The sole comment on this question in the Examination Report is:

“All students were awarded [the] mark for this question.”

Yep, the question is plain stuffed. We think, however, there is more here than the simple wrongness, which is why we’ve made it a WitCH rather than a PoSWW. Happy hunting.

UPDATE (11/05) Steve C’s comment below has inspired an addition:

Update (20/05/20)

The third greatest issue with the exam question is that it is wrong: none of the available answers is correct. The second greatest issue is that the wrongness is obvious: if $z^3$ lies in a sector then the natural guess is that $z$ will lie in one of three equally spaced sectors of a third the width, so God knows why the alarm bells weren’t ringing. The greatest issue is that VCAA didn’t have the guts or the basic integrity to fess up: not a single word of responsibility or remorse. Assholes.

Those are the elephants stomping through the room but, as commenters as have noted, there is plenty more awfulness in this question:

“Letting” $z = a + bi$ is sloppy, confusing and pointless;
The term “quadrant” is undefined;
The use of “principal” is unnecessary;
“argument” is better thought as the measure of an angle not the angle itself;
Given $z$ is a single complex number, “the complete set of values for Arg( $z$ )” will consist of a single number.
The grammar isn’t.

Tag: principal value

WitCH 67: Rooted

UPDATE (29/08/21)

WitCH 37: A Foolproof Argument

Update (20/05/20)