HSC 2016 MX2 Complex Numbers Marathon (archive) (2 Viewers)

Status
Not open for further replies.

math man

Member
Joined
Sep 19, 2009
Messages
503
Location
Sydney
Gender
Male
HSC
N/A
Re: HSC 2016 Complex Numbers Marathon

NEW
Out of scope of course but still fairly doable!
Q. Using Euler's formula e^iz=cis(z) solve the equation sin(z)=2 where z is complex.
 

wu345

Member
Joined
Nov 8, 2014
Messages
96
Gender
Male
HSC
2016
Re: HSC 2016 Complex Numbers Marathon

:( i thought i worked it out for a sec
 

math man

Member
Joined
Sep 19, 2009
Messages
503
Location
Sydney
Gender
Male
HSC
N/A
Re: HSC 2016 Complex Numbers Marathon

:( i thought i worked it out for a sec
1. Find all roots
2. After k=n find all conjugate pairs
3. Group all conjugate pair roots together and factorise using conjugate properties
4. Sub z=-1
5. Factorise all the 2s
6. Double angle formula
7. And you should hopefully see it
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Re: HSC 2016 Complex Numbers Marathon

1. Find all roots
2. After k=n find all conjugate pairs
3. Group all conjugate pair roots together and factorise using conjugate properties
4. Sub z=-1
5. Factorise all the 2s
6. Double angle formula
7. And you should hopefully see it
Step 5 is unnecessary.
 

wu345

Member
Joined
Nov 8, 2014
Messages
96
Gender
Male
HSC
2016
Re: HSC 2016 Complex Numbers Marathon

thanks for the help, I finally got it.
for part b) it's just summing the converging g.p 1/2 +1/4 +1/8+...+1/2n so by the limiting sum of a g.p S=1/2/(1-1/2) which is 1.

Quick Question: What is rep power and what is its significance?

Also - do you just make up these good questions or do you get them from some where?
 

math man

Member
Joined
Sep 19, 2009
Messages
503
Location
Sydney
Gender
Male
HSC
N/A
Re: HSC 2016 Complex Numbers Marathon

thanks for the help, I finally got it.
for part b) it's just summing the converging g.p 1/2 +1/4 +1/8+...+1/2n so by the limiting sum of a g.p S=1/2/(1-1/2) which is 1.

Quick Question: What is rep power and what is its significance?

Also - do you just make up these good questions or do you get them from some where?
Most of these questions are just pretty results found probably from uni which are doable for 4u. However, I have created some original questions before for my tutoring clients, and some are nasty lol
 

porcupinetree

not actually a porcupine
Joined
Dec 12, 2014
Messages
664
Gender
Male
HSC
2015
Re: HSC 2016 Complex Numbers Marathon

thanks for the help, I finally got it.
for part b) it's just summing the converging g.p 1/2 +1/4 +1/8+...+1/2n so by the limiting sum of a g.p S=1/2/(1-1/2) which is 1.

Quick Question: What is rep power and what is its significance?

Also - do you just make up these good questions or do you get them from some where?
Rep power for a particular user is how many reputation points they can give to another user by clicking the reputation button. ie if person X, who has a rep power of 3, decides to give person Y, person Y's overall rep points will increase by 3.

A particular user's rep power depends upon their post count, how long they've been a member (and perhaps how many rep points they have) afaik.
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,662
Gender
Male
HSC
2007
Re: HSC 2016 Complex Numbers Marathon

Here is a one way of proving the fundamental theorem of algebra (given an assumption from slightly outside syllabus).

 
Last edited:

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Re: HSC 2016 Complex Numbers Marathon

Rep power for a particular user is how many reputation points they can give to another user by clicking the reputation button. ie if person X, who has a rep power of 3, decides to give person Y, person Y's overall rep points will increase by 3.

A particular user's rep power depends upon their post count, how long they've been a member (and perhaps how many rep points they have) afaik.
Darn. Now I need to invent a time machine and go back to when BOS first came about, and make my account then.

And then give the details to myself, and then tell him to repeat everything to stabilise the timeline.
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 2)

Top