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For question 3: \text{Let }f(x)=ax^2 + bx +c \\ f^{\prime}(x) = 2ax + b \\ \text{Sub in }x=k, f^{\prime}(k) = 2ak + b, f(k) = ak^2 + bk +c \\ \text{The equation of the line with that gradient and passing through that point it;} g(x)=x(2ak+b) - ak^2 +c. \\ \text{By solving simultaneously, to find...

Re: 1995 Complex Number Problem Wow! Seems much more involved then I thought it would have been. Thanks InteGrand!

Re: 1995 Complex Number Problem Yeah I did, I've fixed it now. How can you be certain that it doesn't "overlap" over the previous roots, such as it is a root but not a "principal" root?

Hi, In the 1999 MX1 paper, question 7 B. How do you do it? Thanks

Hi, I was looking through past papers and found the 1995 MX2 paper question 4 a, and I wasn't sure how to tackle it. The question is; \text{Find the least positive integer k, such that } \cos(\frac{4\pi}{7}) + i\sin(\frac{4\pi}{7}) \text{is a solution to} z^k=1. How do you do it? Thanks

Hi, Has anyone got any good synonyms or alternatives for using the words "discovery", "discovers" and "discoveries"? All I can currently think of is "find" or "found". Thanks

Re: HSC 2017 4U Marathon Is x a real or complex number?

Ok, thank you very much :)

Hi, For annuities the excel textbook has formula's for future and present value, are we meant to use these or just a table of values? Thanks

Hi, I'm interested in the career possibility of being a pure mathematics professor at university. Though I have a few general questions about the career; 1. Once you obtain a degree in pure maths, what's next? Do you get a masters, PHD, further study? 2. How does one become a Mathematics...

Thank you very much for that braintic, I have not seen it proved that way. Thanks InteGrand

Ok, thank you very much. I will not quote the formula

Also, in the syllabus (http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths23u_syl.pdf) page 83 they show the following working out: For (3+5x)^{20}, \frac {t_{k+1}}{t_k} = \frac {5}{3} \frac {20-k}{k+1}. Whilst they don't actually state the formula, the jump from the ratio...

Hi, In the syllabus it states that students should be able to "prove that there are always two square roots of a non-zero complex number". How do you do this? I haven't been able to find anywhere with a good proof and none of my textbooks have it. Thanks

In the sole 4 unit paper? Which question?

How come? Why is it quoted in textbooks such as Fitzpatrick and Margaret Grove?

Hi, Every now and then I run into a problem and solve it using the "usual" methods taught, however I then see a counter example where they attack it in a different way, and in some cases solve the problem much faster. E.g. eddie woo on this binomial identity problem...

Hi, When finding the greatest coefficient in a binomial expansion do I have to algebraically solve \frac {T_{k+1}}{T_k}, or can use that \frac {T_{k+1}}{T_k} = \frac {b(n-k+1)}{ak} in the expansion of (a+b)^n ? Thanks

Hi, I know we are taught the triangle inequalities in complex numbers, but apart from proving them, what questions can be asked from them? Has there been questions previously asked in the HSC using them? Thanks

Hi, I eventually gave up and looked for the answer on the net to question 7 complex numbers in ekman's compilation of questions asking "Simplify \sin(x)+\sin(2x) + \sin(3x) + ... + \sin(nx) ". When I looked at how to derive it, it all involved e^{ix} and t+t^2 +...+t^n = \frac...