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Re: HSC 2013 4U Marathon cbf fixing your working for you. i posted a correct answer with proof above.

Re: HSC 2013 4U Marathon no, that's still wrong.

Re: HSC 2013 4U Marathon lol convenient that you only checked situations with a=1, this is the only time your equation is correct.

Re: HSC 2013 4U Marathon wrong. let theta be zero for example and it doesnt work. heres a better way of rotating parabolas. if we identify complex numbers and the points in the argand plane that represent them, the standard form parabola is given parametrically by: z(t)=2at+iat^2. to...

Re: HSC 2013 3U Marathon Thread you have three dice: die a has sides: 2,2,4,4,9,9. die b has sides: 1,1,6,6,8,8. die c has sides: 3,3,5,5,7,7. 1. what is the average score of die a,b,c respectively. 2. what are the probabilities of: i. a single roll of a being higher than a single roll of...

Re: HSC 2013 4U Marathon did you not read my example of why that logic doesn't work? you are doing exactly the same thing as in my obviously erroneous argument. think about it.

Re: HSC 2013 4U Marathon "Of these infinitely many values of u, cis npi r covers infinitely many of them for infinitely many n" no infinitely many integers are even infinitely many integers are odd therefore there must be infinitely many integers that are both even and odd at the same time qed

Re: HSC 2013 4U Marathon probably shouldnt put qed unless u are sure mate. "cis(nr*pi) is a 'region' of the WHOLE unit circle, that is, every and any complex number will satisfy if and only if r is irrational, this is the converse from the result proven in part (i)" its not true that...

Re: HSC 2013 4U Marathon "That is, the kth term in the sequence must have the same modulus as the nth period of the mth term:" doesn't make sense but the rest is pretty much right. i am quite sure that ii is correct as is.

Re: HSC 2013 4U Marathon fixed, forgot to type pi in.

Re: HSC 2013 4U Marathon .

Re: HSC 2013 4U Marathon something i proved let r be a real number i) prove that the sequence: cis(r*pi), cis(2r*pi), cis(3r*pi),... takes on finitely many values if and only if r is rational. ii) prove that for any complex z with |z|=1 and for any irrational r and for any real c > 0, there...

Re: HSC 2013 4U Marathon not true.

Re: HSC 2013 4U Marathon i dont know man its your question, my ugess is that it works but makes the connection to primes more annoying.

Re: HSC 2013 4U Marathon wouldn't you still be logging something that might be infinity? (and is)

Re: HSC 2013 4U Marathon a couple of questions what does a complex integral mean? if the sum of 1/n is infinity then how can we take its log and use it in inequalities?

Re: HSC 2013 4U Marathon if a quartic has four real roots in AP prove that its derivative has three real roots in AP.