Ekman's Compilation of MX2 Questions (3 Viewers)

[kkk579]

Watch your fucking language potty mouth

aight buddy

 

[WeiWeiMan]

Dyk how to do it

just sub it in lol

z^13 = w
w^11 = z

z = w^11
= z^(13*11) = z^143
hence z^142 = 1
z is some 142nd root of unity
hence z = cos(2πm/142) + isin(2πm/142) for integer m
Im(z) = sin(2πm/142) = sin(πm/71) = sin(πm/n) where n = 71

 

[Average Boreduser]

Yeah i tried that cis form and shit

but yea idfk lmfao. imo just do trial papers or smn instead of some dude's decade old compilations that came from an older syllabus

 

[kkk579]

just sub it in lol

z^13 = w
w^11 = z

z = w^11
= z^(13*11) = z^143
hence z^142 = 1
z is some 142nd root of unity
hence z = cos(2πm/142) + isin(2πm/142) for integer m
Im(z) = sin(2πm/142) = sin(πm/71) = sin(πm/n) where n = 71

whats a root of unity?

 

[SMARTYPANTS_SINGH]

whats a root of unity?

Damn looks like NGO needs to do that

 

[WeiWeiMan]

whats a root of unity?

bro what

an nth root of unity is a complex number of the form z^n=1

these can be written in the form z=cis(2kπ/n) for some integer k

some neat things about roots of unity

sum of roots of unity = 0 {via sum of roots =-b/a}
nth roots of unity can be expressed as 1, w, w^2,..., w^(n-1) where w is some nth root of unity not equal to 1

edit: also, they form regular polygons when graphed in complex plane (argand diagram), (also a cyclic polygon)

 

[SMARTYPANTS_SINGH]

I think u should learn it towards the end of complex

 

[kkk579]

Damn looks like NGO needs to do that

bruh I aint learn this shit yet but the thing is that we only have the locus subtopic left of complex

 

[kkk579]

bro what

an nth root of unity is a complex number of the form z^n=1

these can be written in the form z=cis(2kπ/n) for some integer k

some neat things about roots of unity

sum of roots of unity = 0 {via sum of roots =-b/a}
nth roots of unity can be expressed as 1, w, w^2,..., w^(n-1) where w is some nth root of unity not equal to 1

Yeah nah ngo hasnt taught us that strangely wtf

 

[kkk579]

Yeah nah ngo hasnt taught us that strangely wtf

Bruh ngo needa shape their shit cos wtf. Theres one prac q in the classwork book which mentions z^n=1 but nothing abt the line after which u wrote (expressed as z=cis2kpi/n), but the q isnt even similar to this one its different and doesnt use this root of unity = n concept or whatever

 

[WeiWeiMan]

Bruh ngo needa shape their shit cos wtf. Theres one prac q in the classwork book which mentions z^n=1 but nothing abt the line after which u wrote (expressed as z=cis2kpi/n), but the q isnt even similar to this one its different and doesnt use this root of unity = n concept or whatever

maybe it wasn't useful for it
you don't always need z=cis(2kπ/n) for roots of unity questions
if the question mentioned roots of unity, it contains roots of unity bruv

I used roots of unity for Q10 in the compilation however there may exist different approaches that do not use roots of unity

 

[kkk579]

maybe it wasn't useful for it
you don't always need z=cis(2kπ/n) for roots of unity questions
if the question mentioned roots of unity, it contains roots of unity bruv

I used roots of unity for Q10 in the compilation however there may exist different approaches that do not use roots of unity

Yeah but it was only that one q it wasnt taught explicitly. It was also mentioned in the q to just use z^n=1 so i didnt even actually know that it was roots of unity when i did it

 

[kkk579]

dam. Looks like dr du might do u better it seems.

damn mb ur right

 

[Domain6938]

I think u should learn it towards the end of complex

ag1 crazy rizz brody

 

[sly_lyepat]

does someone have something like this but ext 1 for prelim and year 12

 

[Idk_man122223]

I tried to make some worked solutions to these, seeing as there aren't any already. I didn't include graphs (self explanatory), conics (old syllabus), or mechanics (I haven't learnt it yet). I couldn't do q18 integration, q10 part iii harder 3u, q18 and q20 combinatorics. If you find any issues/have any simpler ways to do any of these please tell me.
(also sorry for the awful formatting, I started with handwriting but it wasn't legible).

 

[tywebb]

combinatorics 20 is



how do i know? it is where is the (n+1)-th Catalan number: https://en.wikipedia.org/wiki/Catalan_number

 

[Idk_man122223]

Thank you, this is the most straightforward answer but I wonder if there is also a reasonable way to do it using concepts more familiar to HSC syllabus.