ChrisNipperHarris Posted May 30, 2012 Report Share Posted May 30, 2012 My conjecture was that the product of the modulus (length) of the roots from the origin equates to n when z^n=1. I managed to prove that but no idea what to do for part B :/ Reply Link to post Share on other sites More sharing options...
ChrisNipperHarris Posted May 30, 2012 Report Share Posted May 30, 2012 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!Autograph is good, just put the imaginary's on the y axis Reply Link to post Share on other sites More sharing options...
TheGlitch Posted June 2, 2012 Report Share Posted June 2, 2012 Okay so i guess there is a little ambiguity on part A, whether the line segments need to be drawn to adjacent roots or all roots. Can someone please help me out ? In another school they have been told that its all the roots!Hi there, the segments are drawn from one root to every other root, with only 1 base root, so for z^n, there'll be n-1 segments Reply Link to post Share on other sites More sharing options...
Cats Posted June 4, 2012 Report Share Posted June 4, 2012 Hello,To those who have done this portfolio, how many pages was yours?To those who are currently doing this portfolio, did your teacher give you a page/word limit? How many pages do you expect to have?My teacher gave us a ten page limit... but I am worried this may not be enough pages. Thanks ! Reply Link to post Share on other sites More sharing options...
LikeA'13OSS Posted June 4, 2012 Report Share Posted June 4, 2012 Theres noway you can do this portfolio in ten pages.........30 pages is the normal for HL Reply Link to post Share on other sites More sharing options...
mavv Posted June 24, 2012 Report Share Posted June 24, 2012 (edited) guys I really need help. I have just started my portfolio. I revised the complex numbers from the fabio ciritto book. However, I am not getting HOW to plot the roots of Z^3=1. what software shall I use? I am already using autograph but I am finding it very tough to understand!! try using Geogebra, it is free to download and automatically plots complex numbers on the argand diagram. I found that I was able to construct the diagrams and measure the distances for n=3,4 and 5 in about 20 minutes. However, measuring the distances is a good start but calculating them leads more easily into proof. Edited June 24, 2012 by mavv Reply Link to post Share on other sites More sharing options...
Ryan Giggs Posted July 12, 2012 Report Share Posted July 12, 2012 Hey guys I need some help with the introduction for this portfolio, I find the task very simple, but I always have trouble starting a piece of work that requires an introduction.Thanks in advance. Reply Link to post Share on other sites More sharing options...
wireman Posted July 14, 2012 Report Share Posted July 14, 2012 When we draw the line segments connecting roots, do we have to draw the segments from one root to the two closest roots only, or line segments from one root to all other roots? Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 15, 2012 Report Share Posted July 15, 2012 Okay people I know there's a lot of argument over to draw roots from one root to all others or to draw segments joining adjacent roots. If this helps by any chance I got an 18/20 on my portfolio which wasn't moderated (unless this went down and my type II went up, which I don't think so anyway coz my mark out of 40 was the same) and I joined adjacent roots and my conjecture had something to do with the lengths of the line segments. 3 Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 15, 2012 Report Share Posted July 15, 2012 And also if I was to give some advice I would say for the lengths try using multiple approaches like a software would add to your technology points but if you did it algebraically it would help you in your last criteria quality of work and also it will help you in criteria C which is to do with what you do to generate a statement. Reply Link to post Share on other sites More sharing options...
pravzcool Posted July 15, 2012 Report Share Posted July 15, 2012 Theres noway you can do this portfolio in ten pages.........30 pages is the normal for HLNo! You'll lose presentation marks if you portfolio is around 30 pages. Trust me. Realistically, it should not exceed 20 - 25 pages. Also, there needs to be more math in the task than words (just as a guide) to get the full presentation marks. Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 15, 2012 Report Share Posted July 15, 2012 Wow mine was 36 for type I and 42 for type II Reply Link to post Share on other sites More sharing options...
wireman Posted July 15, 2012 Report Share Posted July 15, 2012 Okay people I know there's a lot of argument over to draw roots from one root to all others or to draw segments joining adjacent roots. If this helps by any chance I got an 18/20 on my portfolio which wasn't moderated (unless this went down and my type II went up, which I don't think so anyway coz my mark out of 40 was the same) and I joined adjacent roots and my conjecture had something to do with the lengths of the line segments.Okay, that's easy then. . One more question. Do we have to prove that the figures we obtain are polygons with equal sides and equal agains, and do we have to prove that the sum of angles equals 180(n-2) and all that? Or can we just crudely state it? Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 15, 2012 Report Share Posted July 15, 2012 You have to prove the equal lengths of the line segments and the equal sides. The 180(n-2) thing I never did, because I didn't find it relevant to the task anyway. I did what you do for n=3,4 and 5 in terms of n for the conjecture and then to prove it I used factorisation! 1 Reply Link to post Share on other sites More sharing options...
saprativ11 Posted July 19, 2012 Report Share Posted July 19, 2012 I m having hell lot of trouble with the part B, Final 2 tasks! Reply Link to post Share on other sites More sharing options...
saprativ11 Posted July 19, 2012 Report Share Posted July 19, 2012 I m having hell lot of trouble with the part B, Final 2 tasks! Reply Link to post Share on other sites More sharing options...
Ryan Giggs Posted July 23, 2012 Report Share Posted July 23, 2012 I need help with the last 2 tasks, I don't get what they are asking, and I don't understand the difference between a conjecture and a generalization? Reply Link to post Share on other sites More sharing options...
Guest TushieHushie Posted September 9, 2012 Report Share Posted September 9, 2012 Am I allowed to write my conjecture out in words, or do I need an equation/formula? Because I only have it written out. Reply Link to post Share on other sites More sharing options...
macrofire Posted September 9, 2012 Report Share Posted September 9, 2012 Am I allowed to write my conjecture out in words, or do I need an equation/formula? Because I only have it written out.It's always wise to write out your conjecture in both forms to show your thinking and how that translates into an equivalence (or in your case, an equation). Reply Link to post Share on other sites More sharing options...
Nishank Goyal Posted September 13, 2012 Report Share Posted September 13, 2012 Can anyone help me in fguring out the applications of this maths hl portfolio? Reply Link to post Share on other sites More sharing options...
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