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Re: HSC 2013 4U Marathon True that, well is this a good justification? |\langle z,w \rangle|^2=\langle tw, z \rangle \sum_{j=1}^n |w_j|^2 \langle tw, z \rangle \in \mathbb{R} \langle z-tw, z-tw \rangle \geq 0 \therefore \langle tw, z \rangle \leq \langle z, z \rangle \therefore...

Re: HSC 2013 4U Marathon 20=4^2+2^2=(4-2i)(4+2i) \ \ \ 29=5^2+2^2=(5-2i)(5+2i) 20 \cdot 29 = (4-2i)(5-2i) (4+2i)(5+2i) = (16-18i)(16+18i) = 16^2+18^2 \\ \\ 20 \cdot 29 = (4-2i)(5+2i) (4+2i)(5-2i) = (24-2i) (24+2i)=24^2+2^2 (still a question unanswered above)

Re: HSC 2013 4U Marathon (4+i)(5+3i)=17+17i \\ \\ arg(17+17i)=arg((4+i)(5+3i)) \\ \\ \frac{\pi}{4}=arg(4+i)+arg(5+3i) \\ \\ \therefore \frac{\pi}{4}=\tan^{-1}\frac{1}{4}+\tan^{-1} \frac{3}{5}

Re: HSC 2013 4U Marathon \frac{z^6-1}{z-1}=1+z+z^2+z^3+z^4+z^5 \\ \\ = \frac{(z-1)(z-cis \frac{2\pi}{6})(z-cis\frac{4\pi}{6})(z-cis \frac{6\pi}{6})(z-cis\frac{8\pi}{6})(z-cis\frac{10\pi}{6})}{(z-1)}=(z+1)(z^2-2z\cos \frac{2\pi}{6}+1)(z^2-2z\cos \frac{4\pi}{6}+1) Keep in mind my question is...

Re: HSC 2013 4U Marathon Got up to iii, faced a problem: \langle z,w \rangle = t \langle w, w \rangle \\ \\ |\langle z,w \rangle|^2=t \langle w, z \rangle \sum_{j=1}^{n} |w_j|^2 \\ \\ \therefore \langle tw,z \rangle \ \ \in \mathbb{R} \\ \\ \therefore tw=z \\ \therefore $EQUALITY, not...

Re: HSC 2013 4U Marathon Yeah it is subjective but ask yourself where you would see it in an exam. If Q1-3 then easy Q4-6 moderate Q7-8 hard. Beyond HSC yet still in syllabus = Extreme (I guess?)

Re: HSC 2013 4U Marathon HINT: Factorise into 1 linear factor, and 2 quadratic factors. The factorisation you have is among the integers, the one you should have among the irrationals which will be in the form of 1 linear and 2 quadratic factors will have irrational co-efficient EDIT: I...

Re: HSC 2013 4U Marathon $i) Show that $ z^5-1=(z-1)(z^2-2z\cos \frac{2\pi}{5}+1)(z^2-2z\cos \frac{4\pi}{5}+1) \ \ \ \ \ \fbox{2} $ii) Hence form a quadratic equation with roots $ \ \ \ \cos \frac{2\pi}{5} \ \ \ $ AND $ \ \ \ \cos \frac{4\pi}{5} \...

Re: The p00n thread Mainly based on morality of the world how it has changed and mainly WHY is has changed. Whether the world is truly black and white or do interpretations exist or are they just illusions to a boolean world. etc etc

Re: The p00n thread Not from what I've experienced, I have a great plan on what my major work already is, I have most of my research done, I just need to over the holidays prepare the skeleton of the essay, and then the rest of the year, edit and add new things. It's called being efficient.

Re: The p00n thread Yeah it was unjustified of me to call it that easy, but really it does not require much effort, you have the whole year to do the essay/story/whatever with feedback from a teacher. There are barely any tasks and there is no content. I should of probably made clear that when...

Re: The p00n thread Well, I still think that it is something you should really significantly consider 4U maths. I outlined some benefits here I don't want to say that your tutor is giving you bad advice but....yeah

Re: The p00n thread Mainly because 4U english is piss easy, I only dedicate like 1 hour of my time per week to it, I didn't even know when the Viva Voce was, I sat the Viva Voce and did well. And because 4U english is easy, asian parents won't theoretically like that because then they think...

Re: The p00n thread Wait what, nah man you are awesome at maths you should be doing 4U. If you don't it would be a shame tbh (but of course do what you want)

Re: The p00n thread If I wasn't aiming for a 95+ ATAR I would do General Maths anyway (if I couldn't do 2U, 3U or 4U), in my opinion it is always best to have at least some proper mathematical background even if it is as minor as General Math.

Re: The p00n thread Do not even consider General Maths bro Do not even think about it man you will regret doing General

Re: The p00n thread Oh and I am more motivated by failure I think, but only when there is time to fix what had gone wrong. I feel more invigorated and fired up for anything right after I do not do well in it.

Are you motivated by success, or are you motivated by failure? Which one is better? (and why)

Re: HSC 2013 4U Marathon $Given $ \\ \\ e=1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+... \equiv \sum_{r=0}^{\infty} \frac{1}{r!} $Define the nth partial sum $ S_n=\sum_{r=0}^{n} \frac{1}{r!} $i) Explain why $ \ \ \ \frac{1}{k}+\frac{1}{k(k+1)}+...

Omega can mean anything we want it to mean. It means whatever the question specifies it is (at least at MX2 level, not sure if there is some uni math thing utilising omega) Sometimes it is a symbol for roots of unity