# Oxbridge Physics Prelims Revision

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Hoofbeat
Anyone offer any thoughts on this complex no's exam question:

=====
Q. Find the cubix function
Unparseable latex formula:

\fontsize{2} Q(z)

such that
Unparseable latex formula:

\fontsize{2} Q(z) = -1

when
Unparseable latex formula:

\fontsize{2} z=0

and
Unparseable latex formula:

\fontsize{2} Q(z)=0

when
Unparseable latex formula:

\fontsize{2} z=1, e^{2i\pi/3}

and
Unparseable latex formula:

\fontsize{2} e^{4i\pi/3}

=====

So let our cubic equation be:

Unparseable latex formula:

\fontsize{2} Az^{3} + Bz^{2} + Cz + D

Firstly, D=-1 as when z=0, Q(z) = -1.

Then I was thinking that
Unparseable latex formula:

\fontsize{2} z=1, e^{2i\pi/3}, e^{4i\pi/3}

are the roots so if we calculate the sum of these we know they must be equal to -B/A

Similarly work out the product of the roots, ie.
Unparseable latex formula:

\fontsize{2} e^{4i\pi}

we know this must be equal to -1/A and thus
Unparseable latex formula:

\fontsize{2} A = e^{-4i\pi}

. Now I don't know how I should progress?

You just want to write it factorised since you have the factors already by knowing the roots
Unparseable latex formula:

\fontsize{4} Q(z) = A(z-1)(z-e^{2i\pi/3})(z-e^{4i\pi/3})

and since Q(z)=-1 when z=0, so A=1.
Bezza
You just want to write it factorised since you have the factors already by knowing the roots
Unparseable latex formula:

\fontsize{4} Q(z) = A(z-1)(z-e^{2i\pi/3})(z-e^{4i\pi/3})

and since Q(z)=-1 when z=0, so A=1.

Ahhh...so much simpler!

EDIT: Hold on...me being v.stupid....I can't see how you get A=1. As if you set z=0, and Q=-1 you end up with

Unparseable latex formula:

\fontsize{2} -1 = -A \times e^{2i\pi}

now I'm confused!!!!
Hoofbeat
Ahhh...so much simpler!

EDIT: Hold on...me being v.stupid....I can't see how you get A=1. As if you set z=0, and Q=-1 you end up with

Unparseable latex formula:

\fontsize{2} -1 = -A \times e^{2i\pi}

now I'm confused!!!!

but e^(2pi i) =1
RichE
but e^(2pi i) =1

yeah, just use de moivre's - e^(2pi i) = cos(2pi) + isin(2pi) = 1
Willa
still no cookie shiny....I'm tres upset!

wtf?!
Bezza
yeah, just use de moivre's - e^(2pi i) = cos(2pi) + isin(2pi) = 1

of course! thanks
shiny
wtf?!

if it aint there tomorrow i will have to presume they put it in the wrong pigeon hole and some evil person ate it!
Willa
if it aint there tomorrow i will have to presume they put it in the wrong pigeon hole and some evil person ate it!

Or that Shiny never sent it
Willa
if it aint there tomorrow i will have to presume they put it in the wrong pigeon hole and some evil person ate it!

I put £3 in there too!
shiny
I put £3 in there too!

I'm sure it'll be there tomorrow...it has to be!
£3 Expensive pints in cambridge! Willa's going to miss out on the whole ben's cookies experience - you need to have it warm so the chocolate all melts and you forgot to pick up a napkin so have chocolate all over your face
Bezza
£3 Expensive pints in cambridge! Willa's going to miss out on the whole ben's cookies experience - you need to have it warm so the chocolate all melts and you forgot to pick up a napkin so have chocolate all over your face

well he decided that a pint would cost £3. I said it would cost me £1.20 but he still sent me £3, so I was gonna buy the pint and something else with the change and send that back to him
IT CAME. IT CAME. The gift from the dark side came! Yay for shiny, you're the bestest!

Mmm I think I should pop it in the oven for a few mins so I can eat it warm.....mmmmmm cookie!

edit: it's warming in the oven as we speak. Gonna eat it on my way to my compsci lecture. Then I'll be able to judge whether or not it beat's Millies cookies! (I'll keep in mind it's a few days old so wont be as good as when fresh)
I've eaten my cookie now. I have to say, ben's cookies are very very good. It wasnt as "more-ish" as millies cookies are for me (that might be a good thing though cos it saves money) but it definitely had a distinct "homemade" like taste to it, which millies seems to lack. I'd say they're both at least equally as good as each other.
Willa
I've eaten my cookie now. I have to say, ben's cookies are very very good. It wasnt as "more-ish" as millies cookies are for me (that might be a good thing though cos it saves money) but it definitely had a distinct "homemade" like taste to it, which millies seems to lack. I'd say they're both at least equally as good as each other.

Dude get over your Oxford-hating and the true flavour will come through!!!!
~Raphael~
Dude get over your Oxford-hating and the true flavour will come through!!!!

no I'm being objective about this, I don't think you have the right to say I'm not being when you have yet to try millies gourmet chocolate cookie. It's definitely at least as nice. But I agree that there's hardly anything between the two, both taste v yummy!
Willa
no I'm being objective about this, I don't think you have the right to say I'm not being when you have yet to try millies gourmet chocolate cookie. It's definitely at least as nice. But I agree that there's hardly anything between the two, both taste v yummy!

I have tried Millie's Cookies, which is why I was able to make my comment i nthe first place ages ago...Millie's is a crappy chain all over the country in every shopping centre! They're nice, but they have an artificial flavour to them...Of course, this is just my opinion, but I think it's worth more than yours
~Raphael~
I have tried Millie's Cookies, which is why I was able to make my comment i nthe first place ages ago...Millie's is a crappy chain all over the country in every shopping centre! They're nice, but they have an artificial flavour to them...Of course, this is just my opinion, but I think it's worth more than yours

Yeah! In Oxford we have both and Ben's Cookies DEFINITELY outweight Millie's any day!!!
Hoofbeat
Yeah! In Oxford we have both and Ben's Cookies DEFINITELY outweight Millie's any day!!!

or are cookies the new smart drug?

and why isn't cookietasticness in the Guardian league tables?
RichE

or are cookies the new smart drug?

and why isn't cookietasticness in the Guardian league tables?

well the cookie kept me awake longer than normal in my compsci lecture, so it obviously did something!

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