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Portfolio Type I -- Patterns from Complex Numbers


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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

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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

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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 !

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  • 3 weeks later...

:surrender: 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!! :hang:

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 by mavv
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  • 3 weeks later...

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.

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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.

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Theres noway you can do this portfolio in ten pages.........30 pages is the normal for HL

No! 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.

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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. :D . 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?

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  • 1 month later...

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