HSC 2012 MX2 Marathon (archive) (1 Viewer)

Carrotsticks

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Re: 2012 HSC MX2 Marathon

This is a bit of a tricky question.

However looking at the quality of the questions and solutions so far, I'm quite convinced that one of ther 2012'ers will get it:

 

bleakarcher

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Re: 2012 HSC MX2 Marathon

damn...i cant get the second part to that question ^
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

damn...i cant get the second part to that question ^
Hint: Put the RHS into cis form somehow.

Oh and I forgot to type into the question for part (b):



Terribly sorry about that.
 

bleakarcher

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Re: 2012 HSC MX2 Marathon

Consider T(subscript (a))(z)=z/(1+az). Show that T(subscr.(a))(z) constitutes a transformation group by examining the composition T(subcr.(b))(T(subscr.(a))(z))

Go Carrotsticks, try and prove this. I can give you some hints if you want./
Da fuck?
 

bleakarcher

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Re: 2012 HSC MX2 Marathon

It was pretty simple actually that last piece of info was very crucial though.
 

rolpsy

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Re: 2012 HSC MX2 Marathon

Hint: Put the RHS into cis form somehow.

Oh and I forgot to type into the question for part (b):



Terribly sorry about that.
that makes it easier!

(a)



(b)




damn just realised it is supposed to be a plus :confused:

oh silly me, cis(pi) = -1 – fixed.
 
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bleakarcher

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Re: 2012 HSC MX2 Marathon

Why would you give him that question on an mx2 marathon? Are you studying university maths already? Also, Carrotsticks, Im scanning my solution. In part b)it should have been much shorter but i cbf rewriting.
 

SpiralFlex

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Re: 2012 HSC MX2 Marathon

On my iPhone guys so I can't do much. When I get home at around six or seven I will post something cool!
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

Consider T(subscript (a))(z)=z/(1+az). Show that T(subscr.(a))(z) constitutes a transformation group by examining the composition T(subcr.(b))(T(subscr.(a))(z))

Go Carrotsticks, try and prove this. I can give you some hints if you want./
Is this what you mean?



It's conformal field theory. Want to see if Carrotsticks knows. He's at Uni after all.
No, it is not 'conformal field theory'.

It is higher-level algebra, specifically isometries within the Euclidean plane.

Please don't try to sound intelligent by posting up such questions that you most likely just pulled out from the internet. You really are making a fool of yourself.
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

Yes that is what I mean, if the little circle indicates a multiplication. It is part of conformal field theory, specifically the two dimensional conformal group. Physics is the application of mathematics. I find that quite offensive, you think I pulled this off the internet. Look it up. You wont find it.
You are mistaken.

The 'little circle' is the universal symbol for 'function composition'.

Your originally posted question was "composition T(subcr.(b))(T(subscr.(a))(z))"

Then you assert that the 'little circle indicates a multiplication'.

This is what the little circle (in the definition of composition) means:



Going back on track, good work bleakarcher and rolpsy!

However bleakarcher, your method was quite long (and admittedly very illegible as you reached the bottom of the page).
 

bleakarcher

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Re: 2012 HSC MX2 Marathon

You are mistaken.

The 'little circle' is the universal symbol for 'function composition'.

Your originally posted question was "composition T(subcr.(b))(T(subscr.(a))(z))"

Then you assert that the 'little circle indicates a multiplication'.

This is what the little circle (in the definition of composition) means:



Going back on track, good work bleakarcher and rolpsy!

However bleakarcher, your method was quite long (and admittedly very illegible as you reached the bottom of the page).
Yeh, I had a lot of unnecessary working at the bottom of the page since i didnt know what to do until you told me that n=4k, k integral.
 

Carrotsticks

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Re: 2012 HSC MX2 Marathon

Yeh, I had a lot of unnecessary working at the bottom of the page since i didnt know what to do until you told me that n=4k, k integral.
Again, my apologies for causing you grief by forgetting about that little bit of crucial information.
 

SpiralFlex

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Re: 2012 HSC MX2 Marathon

not long



this will help with part i.

I loved this question!

I recall this question from a HSC paper. One of the earlier years.
 
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Carrotsticks

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Re: 2012 HSC MX2 Marathon

Find the radius and centre of the circle that describes the locus of:

 

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