Hyunqul Posted September 6, 2011 Report Share Posted September 6, 2011 For drawing I use wolframe ... but I think there are much better softwares (I think geogebra can work as well). Reply Link to post Share on other sites More sharing options...
dessskris Posted September 6, 2011 Report Share Posted September 6, 2011 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. Reply Link to post Share on other sites More sharing options...
eorxlzjf Posted September 12, 2011 Report Share Posted September 12, 2011 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. For part B, i came up with generalization (conjecture) in an equation. Is this supposed to be an equation? Reply Link to post Share on other sites More sharing options...
dessskris Posted September 12, 2011 Report Share Posted September 12, 2011 yes it is an equation Reply Link to post Share on other sites More sharing options...
eorxlzjf Posted September 12, 2011 Report Share Posted September 12, 2011 yes it is an equationthanks, then it's pretty simple. Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 12, 2011 Report Share Posted September 12, 2011 (edited) A Quick QuestionCan be there 2 different conjectures that both work ...or there is a standard conjecture that everybody should reach ? Edited September 12, 2011 by Hyunqul Reply Link to post Share on other sites More sharing options...
dessskris Posted September 12, 2011 Report Share Posted September 12, 2011 in this task there's only one conjecture, one same conjecture that everyone must get. (you're being asked one conjecture for each part though)usually if you get different results with your friends, it's like you can simplify your answer or maybe you used different variables. Reply Link to post Share on other sites More sharing options...
bomaha Posted September 13, 2011 Report Share Posted September 13, 2011 A Quick QuestionCan be there 2 different conjectures that both work ...or there is a standard conjecture that everybody should reach ?I did this portfolio long time ago, but the teacher didn't correct it. In the first part, I don't want to confuse you but I got 2 different conjectures, and I am 100% sure of the first one and 95% of the second one.And in the second part, you must get a generalization and prove it. Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 15, 2011 Report Share Posted September 15, 2011 (edited) Yeah,there is more than one working conjectutres !!Besides , Part B is confusing ... especially the one before the last ... what I did was testing my obtained conjecture from part A for situations in Part B .... then I dunno wheather I should formulate a new proof or what. Edited September 15, 2011 by Hyunqul Reply Link to post Share on other sites More sharing options...
MahemioHL Posted September 18, 2011 Report Share Posted September 18, 2011 Do we have to find the distances in the first part using cos?? I did it using the distance formula, I still got the same values! I just don't know how to get a mathematical statement as a conjecture! I can put it in words, but not in terms of numbers! Reply Link to post Share on other sites More sharing options...
dessskris Posted September 19, 2011 Report Share Posted September 19, 2011 Do we have to find the distances in the first part using cos?? I did it using the distance formula, I still got the same values! I just don't know how to get a mathematical statement as a conjecture! I can put it in words, but not in terms of numbers!you don't have to. there are many ways, but only one conjecture. so i suppose your method is fine.well the easiest way would be tabulating the values of n and the distance. then you'll see a pattern (or at least you're supposed to see it!). how's the pattern like? any common difference or ratio? work out the general conjecture from there.then, when you want to prove it, simply work with the variable n instead of using numbers. (this method is only for the proof and not to find the conjecture). Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 20, 2011 Report Share Posted September 20, 2011 Can I prove my conjecture geometrically .... or it must be by induction ? Reply Link to post Share on other sites More sharing options...
dessskris Posted September 20, 2011 Report Share Posted September 20, 2011 I honestly don't think you can prove it by induction because there's something about the proposition in maths induction, I can't remember what it is, but it's limiting you from using it in this case. I'm not very sure tbh.what graphically? like you plot n and distance and find regression? I heard it's only acceptable in SL, where in HL you need to be able to prove mathematically i.e. analytically.the proof is very simple. even we discussed it in class when we learnt complex numbers (although we didn't do this task) Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 20, 2011 Report Share Posted September 20, 2011 mm...yeah something near that .One more question , plz , does IBO inform the teacher about the true steps of the IA ? In other words , should I trust all my teacher's guidance in this IA ? cuz sometimes I think that his instructions are not enough or satisfactory. Reply Link to post Share on other sites More sharing options...
dessskris Posted September 21, 2011 Report Share Posted September 21, 2011 I can't be sure, however what I know is that teachers are asked to do the IA task too although they don't produce a portfolio. they just work out the thing and show the working etc. then a number of IAs from your batch will be sent for moderation and the teacher's work will also be sent to the moderator. so if the students write exactly the same thing as the teacher then the moderator will be suspicious. or if your teacher does the task wrongly and everyone makes the same mistake, well the moderator might do something about it.another thing I know is that there's a forum from the IBO for all IB teachers. so in this IB forum all teachers can share their findings on the IA task and discuss the answers.what is it that your teacher told you that you think is wrong? 1 Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 22, 2011 Report Share Posted September 22, 2011 My teacher told me that generalizing and proving my results for Z^n=a+bi where their modlus is 1 is only requiring testing my conjecture obtained from Part A with those values which modlus is 1 ... if the conjecture works for all of them ... then this is the proof ... and all what I have to do is writing a statement generalizing my conjecture from part A saying that it works for all values where their modlus is 1.But Ithink that I have to formulate a new conjecture or equation in Part B ... right? I'm so confused. Reply Link to post Share on other sites More sharing options...
dessskris Posted September 23, 2011 Report Share Posted September 23, 2011 from part A you generalise and then PROVEpart B deals with something different, you don't use the distance equation for part B. maybe your teacher said it wrongly? 1 Reply Link to post Share on other sites More sharing options...
Hyunqul Posted September 23, 2011 Report Share Posted September 23, 2011 Yeah that what I was told ... and what I did...I used the distance formula !!!SO , all my work in part B is flawed ? Reply Link to post Share on other sites More sharing options...
dessskris Posted September 24, 2011 Report Share Posted September 24, 2011 it depends on how it turned out! were you able to prove the thing using the distance formula? I honestly don't think so! so yeah maybe...you need to restart your part B Reply Link to post Share on other sites More sharing options...
K.Hosny.M Posted September 28, 2011 Report Share Posted September 28, 2011 Friends pleaseRegarding the Part B in the IAThere is a very big miss-understanding happened to meso pleasetell me exactly what is meant by the last two points in the Part Bwhich says1- Generalize and prove your results for zn=a+bi , where |a+bi|=1.2- What happens when |a+bi|not = 1?THANKS Reply Link to post Share on other sites More sharing options...
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