PoSWW 4: Overly Complex

This PoSWW comes courtesy of a smart Year 11 VCE student who, it appears, may be a rich source of such nonsense. It’s an exercise in the Jacaranda text MathsQuest 11, Specialist Mathematics (2019).

To be honest, we’re not sure the exercise below is a PoSWW. It may simply be a minor error, the likes of which are inevitable in any text, and of which it is uninteresting and unfair to nitpick. But, for the life of us, we have no idea what the authors might have intended to ask. Make of it what you will:

UPDATE: For those hoping that context will help make sense of the exercise, the section of the text is an introduction to factoring over complex numbers. And, the text’s answer to the above exercise is A = 2, B = 5, C = -1, D = 2.

15 Replies to “PoSWW 4: Overly Complex”

  1. I think having a context of preceding questions, together with knowing the section of theory those questions relate to, would shed some light on the authors intent.

    Some thoughts and opinions:

    1. The A is redundant unless, bizarrely, some sort of parametric solution for A, B, C and D is required.

    2. It might just be a grotesque motivation for expanding the denominator of the RHS.

    3. If it’s part of the complex numbers chapter, I don’t see the point in using x rather than z as the variable.

    4. I agree with your assessment of the question, except for your use of the word minor and your implication of singular when remarking on errors …. However, I’d go a bit stronger and assess the question as chicken vomit.

    5. MathsQuest is getting a lot of free publicity – I guess they subscribe to the Oscar Wilde proverb “The only thing worse than being talked about is not being talked about”

    6. The smart Yr 11 VCE student should throw away MathsQuest and do the questions from Cambridge.

    1. Agree. Unless there is a restriction on what A, B, C and D are allowed to be (integers, rational, real, multiples of 42) then the question is infinitely pointless.

  2. John, I’ve updated the post to indicate the context. I don’t think it helps. Number 8, even if one is demanding the unknowns be integers, the point of the question escapes me.

  3. Yep, it looks pretty POSWW-ish. But I’m still puzzled. The authors were intending something, but I can’t imagine what.

    1. OK, be puzzled and imagine no more. Here’s what the authors intended (which is NOT reflected in either the question nor the answer):

      …. find A, B, C and D *where each is a purely imaginary integer*.

    1. I’m not quite sure what you mean. (I’m also not quite sure why you’re trying to make sense of this nonsense.) You mean because there’s a family of solutions? How would you phrase the question or write the solution(s) to be somehow sensible?

      1. I wouldn’t but I feel it improves the question a bit to write “can be written in the form” instead of using an equation.

  4. I agree with John’s comments that A is redundant unless a parametric solution of
    A = 1/t ,B = 5t C = -t D = 2t is required where t not = 0.

    Perhaps point of question is merely to recognise denominators are equivalent and equate coefficients of powers of X to obtain values given in solution with t =1?

      1. Maybe but that’s not much of a point. It can be thought of as a precursor to partial fractions, except the fractions are nowhere in sight and haven’t been covered yet, you’d begin with non-complex factors, school students would probably never require partial fractions with complex fractions and the A is still redundant.

  5. The A is pointless (and creates an excessive degree of freedom), but the whole question is kind of strange.

    All you’re doing is looking at that complicated mess and then factoring out a 2 from the denominator. I would think they instead meant to do some sort of partial fractions stuff, no, where you solve for numerators?

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