Firemarshall Posted February 25, 2012 Report Share Posted February 25, 2012 I found my conjecture but how do i prove it??Through Induction or any other method??? Reply Link to post Share on other sites More sharing options...
Justin Lee_47547 Posted March 4, 2012 Report Share Posted March 4, 2012 Hi, I am now doing the same IA, but have encounter some misunderstanding Part B. I found Part A quite easy, and have came up with a conjecture and proved it via different ways. Yet in Part B, the part about Generalize and prove your results for zn=a+bi where modulus =1 , I don't quite understand what they want to find. I know what generalizing is, so please don't get mad just yet ! From what I have found from previous investigation, I can only conclude that zn=a+bi will be cis(smth) and that angle is between 2 values that i know. Is that all they are asking from us? Can i answer the question saying that there is a range of possible answers there? Thanks, please help me, IA is dued in half a day, and I still pulling my hair trying to understand their expectations. Never mind, solved my problem. 1 Reply Link to post Share on other sites More sharing options...
mayank06090 Posted March 10, 2012 Report Share Posted March 10, 2012 arghhh not getting the link between the values and distance between roots for part A....someone please help Reply Link to post Share on other sites More sharing options...
musicforlife1595 Posted March 12, 2012 Report Share Posted March 12, 2012 Hey, I have the same portfolio this year, so could someone help me out with my conjecture. I have come up with sumthing, but i highly doubt its correct . i could message it to someone, maybe ?Help.please. Reply Link to post Share on other sites More sharing options...
musicforlife1595 Posted March 12, 2012 Report Share Posted March 12, 2012 I found my conjecture but how do i prove it?? Through Induction or any other method??? Hi, I am now doing the same IA, but have encounter some misunderstanding Part B. I found Part A quite easy, and have came up with a conjecture and proved it via different ways. Yet in Part B, the part about Generalize and prove your results for zn=a+bi where modulus =1 , I don't quite understand what they want to find. I know what generalizing is, so please don't get mad just yet ! From what I have found from previous investigation, I can only conclude that zn=a+bi will be cis(smth) and that angle is between 2 values that i know. Is that all they are asking from us? Can i answer the question saying that there is a range of possible answers there? Thanks, please help me, IA is dued in half a day, and I still pulling my hair trying to understand their expectations. Either of you, any help with - -the conjecture in part A -the factorising -the generalistion in part B would be highly appreciated. Im assuming you guys are done, so it would be awesome if you could help Reply Link to post Share on other sites More sharing options...
Jaysong Posted March 12, 2012 Report Share Posted March 12, 2012 Contradicting from what I've read so far on this thread, the common idea here that the conjecture would concern the perimeter of the polygon formed within the unit circle is, according to our HL maths teacher, not the correct thing to look for. This is because that conjecture is pretty obvious, and the thing IBO is looking for is more interesting and unintuitive. Also, in Part A, you are supposed to draw line segments connecting one chosen root with all other roots, rather than drawing line segments connecting adjacent roots, forming a polygon. Now the question is, HOW THE HELL AM I SUPPOSED TO FIND A CONJECTURE ON THE LENGTHS OF THESE LINE SEGMENTS CONNECTING ALL ROOTS TO ONE CHOSEN ROOT? Reply Link to post Share on other sites More sharing options...
musicforlife1595 Posted March 13, 2012 Report Share Posted March 13, 2012 Contradicting from what I've read so far on this thread, the common idea here that the conjecture would concern the perimeter of the polygon formed within the unit circle is, according to our HL maths teacher, not the correct thing to look for. This is because that conjecture is pretty obvious, and the thing IBO is looking for is more interesting and unintuitive. Also, in Part A, you are supposed to draw line segments connecting one chosen root with all other roots, rather than drawing line segments connecting adjacent roots, forming a polygon. Now the question is, HOW THE HELL AM I SUPPOSED TO FIND A CONJECTURE ON THE LENGTHS OF THESE LINE SEGMENTS CONNECTING ALL ROOTS TO ONE CHOSEN ROOT? That's The exact bombshell our math HL teacher dropped on us today. The conjecture HAS to be based on the lenghts connecting all roots to one paticular root. I see no link now, and here I was thinking I have my conjecture /: ideas, anyone?Ohh and one more thing , what exactly are we gaining out of the factorisaion ? I do not understand . Reply Link to post Share on other sites More sharing options...
Jaysong Posted March 13, 2012 Report Share Posted March 13, 2012 Yeah, I'm completely lost also. I think the conjecture is related to the factorization. We should see some kind of link/pattern between the factors obtained and the lengths derived. Reply Link to post Share on other sites More sharing options...
musicforlife1595 Posted March 13, 2012 Report Share Posted March 13, 2012 Hi i need help with the conjecture part in part ASpecify please; you can deduce a conjecture if you got the lengths between roots of the equation z^n - 1 = 0 for n = 3, 4, 5. Generalize the solutions to get your conjecture. Do the same as you did with numbers but use "n" variable.there doesnt seem like there is a pattern, specially when you connect one root to all others. Any more advice ? Reply Link to post Share on other sites More sharing options...
Jaysong Posted March 14, 2012 Report Share Posted March 14, 2012 Can anyone please tell me the conjecture, I am not shure whether my one is correct or notYou could ask your teacher and see whether your teacher thinks the conjecture is the right one or not.Anyways, for other people, the conjecture is related to the lengths of line segments connecting one chosen root with all other roots - NOT the line segments connecting adjacent roots forming a polygon. My hint would be to make a table on the lengths of these line segments, and try to somehow derive the value of n using the lengths for each. The conjecture is not super-complicated, so don't think too complex. Reply Link to post Share on other sites More sharing options...
bro22 Posted March 26, 2012 Report Share Posted March 26, 2012 A couple of questions guys. First of all is there any decent software that can graph complex numbers and draw line segments? use Autograph, it's PERFECT! 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. didn't your teacher tell you what the modulus sign means? it's the magnitude meaning when you express the complex number in cis form, it's only cis(θ) instead of kcis(θ) since your k is 1 here. meaning there's not only four possibilities. 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! generalise like what i said. Hi . Can the conjecture for Part A contain sin or cos in it? Would really appreciate your advice on this matter! Thanks Reply Link to post Share on other sites More sharing options...
Jaysong Posted March 31, 2012 Report Share Posted March 31, 2012 can anyone send the entire task? The entire task can be found on this thread. Forgot what page it was on, but you'll find it by browsing through the pages of this thread. Reply Link to post Share on other sites More sharing options...
Evan Luthra Posted April 1, 2012 Report Share Posted April 1, 2012 i have almost completed mine but i just wanted to verify and needed some help with the scope and limitations . , someone can please send me thier complete portoflio to have a look ?Ps. I also use macbook air . so can someone refer some graph programs for mac . ?The grapher one doesnt let me graph the unit circle .i have autograph , but dont know how to use it .. any help wouldbe appreaicated . thanks .Also, can someone give an idea of what scope and lmiitations are present in this assignment. Reply Link to post Share on other sites More sharing options...
j.raichura Posted April 6, 2012 Report Share Posted April 6, 2012 Well even i am doing my portfolio on Complex numbers and have got the congecture successfully.Hmm the only thing i can say is that why dont you all compare and analysize the lenghts you'll get while working on the de movier;s theorem.See what all lenghts you get from the roots and wirte it seperately. Work it out accordingly and am sure the moment you'll find your conjecture there'll be a huge smile on everyone's face as it seems to be difficult which actually is not. 1 Reply Link to post Share on other sites More sharing options...
Animesh Posted April 12, 2012 Report Share Posted April 12, 2012 i have the same portfolio. i am haveing problems formulating the conjecture (part 5 of part A). I dont understand what kinda conjecture we need to come up with. is it a conjecture that shows the relation between the angles adn the line segments? i know i suck . pls help Reply Link to post Share on other sites More sharing options...
krakaton Posted April 12, 2012 Report Share Posted April 12, 2012 I've gotten all my conjectures together and I know that they're right. I was just wondering if anyone could provide some help on how to prove them?Just tell me the method to use, induction or something else. Reply Link to post Share on other sites More sharing options...
Capricious Posted April 14, 2012 Report Share Posted April 14, 2012 I have a conjecture for Part A, with proof, but I have no idea whether it's even on the right track? Someone here who could take a look at my answer and tell me if it's right or not? Reply Link to post Share on other sites More sharing options...
krakaton Posted April 16, 2012 Report Share Posted April 16, 2012 Little bit of advice to everyone busting their heads over the proof - it's probably not going to happen.The proof is only 1 mark out of 20, the remaining 19 are for good communication, intelligent working and a good assessment of the scope and limitations of the conjecture.Spend your time on making that 19/20 portfolio and once you're done, then try prove it to try to get that perfect score. Reply Link to post Share on other sites More sharing options...
TogoPogo Posted April 19, 2012 Report Share Posted April 19, 2012 I think that you could come up with ANY conjecture... and since N is a positive integer, it is easier to prove it using Mathematical Induction. PS: thats a nice conjecture.. I would disagree. they're asking us to conjecture the lengths of the line segments in part A and roots of complex numbers in part B. This post has nothing to do with what you just said up there^, but I just wanted to thank you for taking time out of your day to help us with our portfolios. I have a better idea of how to approach this now that I've read through your comments Reply Link to post Share on other sites More sharing options...
pigletbabe Posted April 21, 2012 Report Share Posted April 21, 2012 The lengths of the segments of the roots have no pattern, or at least I can't find any.z3=1, the segments are square root 3z4=1, square root 2 and square root 4however, z5=1 isn't square root 1.Can anyone tell me how I can find a pattern in this? Reply Link to post Share on other sites More sharing options...
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