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Re: HSC 2013 4U Marathon a) z+z^2+...+z^n=z[z^n-1]/(z-1) Let z=cis(w_j). => cis(w_j)+[cis(w_j)]^2+...+[cis(w_j)]^n=cis(w_j)[[cis(w_j)]^n-1]/(z-1) i.e. cis(w_j)+cis(2w_j)+...+cis(nw_j)=cis(w_j)[cis(nw_j)-1]/(z-1) by de Moivre's theorem =cis(w_j)[cis(n[2pi*j/n])-1]/(z-1)=0 => sum from t=1 to n...

Re: HSC 2013 4U Marathon That's t^n-1.

Re: HSC 2013 4U Marathon I don't think the factorisation over Q is correct. You are not given whether n is even or odd.

lol. yeah thanks bro, you too in all your exams.

Re: HSC 2013 4U Marathon Well yeah pretty much. My class has already finished Complex Numbers and almost finished Graphs.

Re: HSC 2013 4U Marathon Notice the point (0,0) representing z=0 lies on the circle lz-1l=1, initially we were given (1/z)+(1/conjugate(z))=1 and so z=/=0.

Problem with that question though is that you can no longer assume g is constant as it begins falling after it reaches max. height really. It should increase significantly as it falls closer to the surface of the planet. It works obviously if you assume that g does stay constant though.

Re: 2013 HSC Students - heed my/our warning regarding Engineering Studies as a subjec Didn't run in mine either, thank god it didnt..

lol, thought it wasn't clear enough too.

I can answer the first part (I think haha). Is 'g-force is a measure of the ratio of the apparent weight of an object to its true weight' sufficient?

lol shit, I didn't know. I thought they would have marked you down for saying object..

a mass* lol

Do any of you guys know the name of this effect where the Earth bulges because of its rotational velocity? Want to look into it.

orite, thanks for confirming bro.

That's what I'm thinking..

Sorry, just a question. Wouldn't a decrease in rotational velocity result in a lower radius and hence an increased value of g?

Btw guys that 'proof' of Euler formula I actually found once in an MX2 trial paper haha, they need to start introducing more rigour into the course..

I don't even make any notes tbh, not bothered for that shit. I'm just reading out of textbooks and other notes. I find that a lot of people end up writing their notes and just wasting their time when they realise that in writing their notes they haven't really gained too much knowledge. The...

I don't even make any notes tbh, not bothered for that shit. I'm just reading out of textbooks and other notes. I find that a lot of people end up writing their notes and just wasting their time when they realise that in writing their notes they haven't really gained too much knowledge. The...

It is used in the Cambridge 4U textbook though.