Jump to content

Portfolio Type I -- Patterns from Complex Numbers


Recommended Posts

hey guys why no one is answering me :(

i need you help guys please come on.

oh sorry... it's because it seems like you're not putting enough effort into it... :ateeq: anyway if you need me to reply, quote my post so i get a notification.

guys please i need help

i am stuck at bullet number 7,8

* Use graphing software to test your conjecture for some more values of n and make modifications to your conjecture if necessary.

* Prove your conjecture.

and in part B

in the last two bullet

please anyone tell me how to generalize ????

what do they mean by this ?

and what happens when |a+bi| not equal 1 ??

please help guys

thanks

for the graphing software, try autograph. it's awesome and is useful for this task.

for the proving part, work with the variable n instead of with numbers.

generalising is like:

(this is just a random example)

when n=1, m=2

when n=2, m=5

when n=3, m=10

when n=4, m=17

when n=5, m=26

you see some pattern there? when you generalise it, you'll get m=n²+1. just like that.

when |a+bi|≠1, well, you try and do it yourself and you'll see what happen...

Edited by Desy Glau
Link to post
Share on other sites

  • 1 month later...

hey guys why no one is answering me :(

i need you help guys please come on.

oh sorry... it's because it seems like you're not putting enough effort into it... :ateeq: anyway if you need me to reply, quote my post so i get a notification.

guys please i need help

i am stuck at bullet number 7,8

* Use graphing software to test your conjecture for some more values of n and make modifications to your conjecture if necessary.

* Prove your conjecture.

and in part B

in the last two bullet

please anyone tell me how to generalize ????

what do they mean by this ?

and what happens when |a+bi| not equal 1 ??

please help guys

thanks

for the graphing software, try autograph. it's awesome and is useful for this task.

for the proving part, work with the variable n instead of with numbers.

generalising is like:

(this is just a random example)

when n=1, m=2

when n=2, m=5

when n=3, m=10

when n=4, m=17

when n=5, m=26

you see some pattern there? when you generalise it, you'll get m=n²+1. just like that.

when |a+bi|≠1, well, you try and do it yourself and you'll see what happen...

Hey friend

please tell me what they need in the conjuncture in details and what do they mean by it ?

and regarding the generalize please give me one example only when Z=4 or when Z = whatever because i don't know how to start

Thanks

Link to post
Share on other sites

the first one they need you to conjecture the distance from one root to another. it's some kind of formula.

you can't generalise from only 1 example.

I can't give you any answer.

if you don't know how to start then it's either you have a bad teacher or you never listen to them. my teacher, not knowing it's being asked in this IA, has explained how to find roots of complex numbers when we learnt this chapter. or you should be able to find it in your textbook.

Link to post
Share on other sites

the first one they need you to conjecture the distance from one root to another. it's some kind of formula.

you can't generalise from only 1 example.

I can't give you any answer.

if you don't know how to start then it's either you have a bad teacher or you never listen to them. my teacher, not knowing it's being asked in this IA, has explained how to find roots of complex numbers when we learnt this chapter. or you should be able to find it in your textbook.

No man i meant i didn't start in the generalizing bullet not in the conjuncture !

Link to post
Share on other sites

No man i meant i didn't start in the generalizing bullet not in the conjuncture !

huh? what are you trying to say? I don't quite understand.

when you generalise, you get the conjecture. so you're basically hinting at the same thing.

Man the conjucture is in part 1

the generalizing is in PART 2 !

Link to post
Share on other sites

yes there are two parts but what I'm trying to say is when you generalise, you get a conjecture. so basically they ask about the same thing but they ask for different conjectures and in different ways.

are you here just to fight with me or to ask a question?

What are you saying man :) of-course to ask

i really i need some help

i want to know only how to generalize ?

that's what am asking about

and i hope to get an answer

just give me one real example

thanks

Link to post
Share on other sites

ok... a random example.

when n=1, L=0

when n=2, L=1

when n=3, L=4

when n=4, L=9

when n=5, L=16

...

so after doing some calculation and working etc you can get L=n²-2n+1. you can do matrices or graphing, anything (perhaps algebraically since you're in HL) to get a conjecture.

Hi there, im currently doing this IA, and need to get it finished asap

I came up with a conjecture for finding the length of the distances between 2 adjacent vertices, of an n sided polygon for zn. when plotting the roots zn on an argand diagram in autograph, it looks like a n sided regular polygon, with angles 2 π/n or (360/n) ⁰ between the vectors from the origin to each n vertices. See pic url for the plots.

http://imageshack.us/photo/my-images/20/nthrootsofunity.png/

My conjecture, after checking with measurements from autograph, works when tested with more n values. However, i need to prove that for n being a positive integer, that z n gives a regular polygon with n vertices, so angles between are equivalent to 2 π/n or (360/n) ⁰. Yes we can visually see that on the graph, but how do we algebraically prove this?

Any help is incredibly appreciated. For anyone out there wanting an answer, Please dont ask me to give you my conjecture, as i spent ages on this IA.

  • Like 1
Link to post
Share on other sites

first off i suggest you to put separate graphs for each value of n. the examiner or your teacher will be confused.

I'm so sorry I can't tell you how, because it's the answer to this IA however i can give you hints.

you know how to find roots of complex numbers? I bet your teacher has taught you or at least it's in your textbook. convert it to cis form first. you know what you do to the magnitude and to the angle? how do you do it? for example, z^3=2i+7. are you familiar with this? yes? then you know how to solve z^3=1, right? then do it for z^n=1. just treat n, your variable, like a constant and find the solutions.

for the polygon part, didn't your teacher tell you that roots of complex numbers are always equally spaced from the adjacent roots? from there you can conclude that they always form polygons.

good luck with the rest of the IA! you know you could've asked me ages ago if you need.

and yeah, never give your conjecture to anyone.

Link to post
Share on other sites

first off i suggest you to put separate graphs for each value of n. the examiner or your teacher will be confused.

I'm so sorry I can't tell you how, because it's the answer to this IA however i can give you hints.

you know how to find roots of complex numbers? I bet your teacher has taught you or at least it's in your textbook. convert it to cis form first. you know what you do to the magnitude and to the angle? how do you do it? for example, z^3=2i+7. are you familiar with this? yes? then you know how to solve z^3=1, right? then do it for z^n=1. just treat n, your variable, like a constant and find the solutions.

for the polygon part, didn't your teacher tell you that roots of complex numbers are always equally spaced from the adjacent roots? from there you can conclude that they always form polygons.

good luck with the rest of the IA! you know you could've asked me ages ago if you need.

and yeah, never give your conjecture to anyone.

Thank you for the advice :D! Yep i shall have another go, even though Maths is a paaaaaaiiiiinnnn......

Link to post
Share on other sites

I have a question regarding point 2 in Part B :

( Generalize and prove your results for | a+bi | =1 .... what is actully required?

Shall there be a new conjecture different from that one obtained in part A?

Is it concerning the distance between roots of unity as well as part A?

Or it is just the generalization that z = cos(*)+isn(*) ?

Link to post
Share on other sites

A couple of questions guys. First of all is there any decent software that can graph complex numbers and draw line segments? And secondly in the second part of the IA we're told to generalise and prove for z^n=a+bi where mod(a+bi)=1..so what I'm unsure about is if mod (a+bi) is 1 there's four different possibilities that is z^n=1,-1,i or even -i. So now do we have to generalise and prove for every one of those or just i since the first two questions r about i? If its just i then this is insanely easy!

Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...