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Portfolio Type I -- Patterns from Complex Numbers


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Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

Just do it, even if it has no use in your portfolio. You don't want to lose some points on something that is so easy.

Agreed. The markers will just look at it as if you've skipped something that needs to be done, and will dock marks accordingly.

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When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5

does it mean that we're joining lines from 1 point to the other points?

from a point to two neighbouring/adjacent points.

Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

you HAVE to answer every single question and in the correct order.

the factorising part is necessary. for what? for them to see your capabilites. besides, it can be used to validate your conjecture.

everything they told you to do has some use.

as the others have also said, you'll get penalised if you skip any bullet point.

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When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5

does it mean that we're joining lines from 1 point to the other points?

from a point to two neighbouring/adjacent points.

Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

you HAVE to answer every single question and in the correct order.

the factorising part is necessary. for what? for them to see your capabilites. besides, it can be used to validate your conjecture.

everything they told you to do has some use.

as the others have also said, you'll get penalised if you skip any bullet point.

I spoke to my teacher about this and he said there is no problem with skipping or rearranging the format of the portfolio... Because they are only a guideline to investigate and find patterns in complex numbers....

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When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5

does it mean that we're joining lines from 1 point to the other points?

from a point to two neighbouring/adjacent points.

Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

you HAVE to answer every single question and in the correct order.

the factorising part is necessary. for what? for them to see your capabilites. besides, it can be used to validate your conjecture.

everything they told you to do has some use.

as the others have also said, you'll get penalised if you skip any bullet point.

I spoke to my teacher about this and he said there is no problem with skipping or rearranging the format of the portfolio... Because they are only a guideline to investigate and find patterns in complex numbers....

It's better to go with portfolio order. You don't want the moderator to be :dontgetit: . The order they put is to get the conjecture step by step. In the end, it's your choice if you want to rearrange/skip the question asked.

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Just to make sure, Part A bullet point 2, after plotting these roots, you will see an isosceles triangle?

"choose a root and draw" bullet point 3, how to do that on autograph?

How did you measure the line segments? by a ruler?

What to comment on the results?

How to measure the length of the roots of z^5 - 1 =0?

equilateral triangle.

click one point, hold Shift while clicking the other point. right click, line segment. it'll also give you the length of the line in the Results Box.

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Hi i need help with the conjecture part in part A

Specify 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.

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  • 2 weeks later...

Hi i need help with the conjecture part in part A

Specify 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.

do we plot the equations on the same graph ?

When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5

does it mean that we're joining lines from 1 point to the other points?

from a point to two neighbouring/adjacent points.

Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

you HAVE to answer every single question and in the correct order.

the factorising part is necessary. for what? for them to see your capabilites. besides, it can be used to validate your conjecture.

everything they told you to do has some use.

as the others have also said, you'll get penalised if you skip any bullet point.

I spoke to my teacher about this and he said there is no problem with skipping or rearranging the format of the portfolio... Because they are only a guideline to investigate and find patterns in complex numbers....

It's better to go with portfolio order. You don't want the moderator to be :dontgetit: . The order they put is to get the conjecture step by step. In the end, it's your choice if you want to rearrange/skip the question asked.

do we plot the equations on the same graph ?

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  • 2 weeks later...

When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5

does it mean that we're joining lines from 1 point to the other points?

from a point to two neighbouring/adjacent points.

Do we have to follow the bullet points on the portfolio? Can we mix up to a certain way that is neater to me and it makes more sense?

Also for example, in my case I believe that there was no need for factorizing z^n-1=0 for n =3,4,5

Can we skip it if there was no use for it in my portfolio.

you HAVE to answer every single question and in the correct order.

the factorising part is necessary. for what? for them to see your capabilites. besides, it can be used to validate your conjecture.

everything they told you to do has some use.

as the others have also said, you'll get penalised if you skip any bullet point.

I disagree with the first answer, it says "choose a root and draw line segments from this root to the other two roots", you choose one root and link it with the others, not link it with the adjacent roots, although I think like people have said before it doesn't really matter as what way you interpret the information as long as you use it in some way to investigate patterns of complex numbers

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Good luck with your portfolios everyone!

I am quite inexperienced with these stuff so I have a question, which might be very stupid. I was wondering if I could take a different (?) approach at some point of this task and make use of a vector property, i.e: dot product. I know that we are expected to work out a pattern in complex numbers, but wouldn't complex vectors apply too, really?

Thanks in advance.

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Hi there.

I draw a line segment from one root to another but i could not measure the magnitude of this line segment. how can i measure it?

Just apply the cos theorem and you'll work it out pretty easily.

Can there be a trigonometric expression in the conjecture? If so, then it is extremely easy, but I don't know if that is the correct one.

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Hey guys..what exactly are you supposed to generalise in part B? I dont get it, is it the conjecture about the distance between the roots of z??????

Hey,you need to identify a root and draw line segments from this root to other roots and study a pattern of the distance from this root to the other roots for all values of n.

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Hi there.

I draw a line segment from one root to another but i could not measure the magnitude of this line segment. how can i measure it?

Just apply the cos theorem and you'll work it out pretty easily.

Can there be a trigonometric expression in the conjecture? If so, then it is extremely easy, but I don't know if that is the correct one.

Use geogebra software.

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  • 2 weeks later...

hi guys,

Just got the portfolio,

I found everything Part A easy, until I had to prove my conjecture, which is composed of two parts:distance between adjacent roots, and area of polygon. I do not know how to prove? Would induction suffice? I am trying to prove via tabulation on excel, would that be alright? if i show that whatever the value of n, formula holds. I have seen a few limitations, they are fairly obvious, hint- same limitations as de moivre's since we derived it from there.

I do not understand how to form a conjecture by genaralizing in part b.

Could anyone help me out? maybe check my conjecture? would appreciate it highly.

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