dessskris Posted June 7, 2011 Report Share Posted June 7, 2011 area? am I missing something or are you doing extra work? you don't need to work out the area of the polygon do you?your conjecture is like the general statement of the length or distance between two roots (part A) and the roots of the complex numbers (part B). the former involves cos, the latter is just using some cis stuffs.to prove it, you can do exactly the same thing that you did with each value of n, now with the variable n instead of numbers. Reply Link to post Share on other sites More sharing options...
Gnick Wright Posted June 8, 2011 Report Share Posted June 8, 2011 I used a program called geogebra, which calculated the area for me automatically. I also used microsoft excel as a program to calculate my values for z^n-1, using =COS(k*2*PI()/n) for a and =SIN(k*2*PI()/n) for b where z^n = a+bi (anyone else whos doing the IA should do this, it makes things alot less tedious) but i havent gotten to the second half of the IA yet. 1 Reply Link to post Share on other sites More sharing options...
bomaha Posted June 8, 2011 Report Share Posted June 8, 2011 I used a program called geogebra, which calculated the area for me automatically. I also used microsoft excel as a program to calculate my values for z^n-1, using =COS(k*2*PI()/n) for a and =SIN(k*2*PI()/n) for b where z^n = a+bi (anyone else whos doing the IA should do this, it makes things alot less tedious) but i havent gotten to the second half of the IA yet.I've done this IA, and I don't think that you need to calculate the area. For part A, you just need to get the distances between the roots of the given equations, get a conjecture, and prove the conjecture. 1 Reply Link to post Share on other sites More sharing options...
DDuino Posted June 17, 2011 Report Share Posted June 17, 2011 guys..have you actually thought about limitations?i have been told to pay close attention to the mark scheme..in generalization you would need to write the limitations if you carefully read...and this then mean what happens if the n is zero or any negative number...have you thought about it?i think very important even though is not stated in the IA as a bullet point Reply Link to post Share on other sites More sharing options...
dessskris Posted June 18, 2011 Report Share Posted June 18, 2011 yes it is true. thanks. there are some limitations that I could think of, some are important and some are not. Reply Link to post Share on other sites More sharing options...
jaisaha94 Posted June 20, 2011 Report Share Posted June 20, 2011 I used a program called geogebra, which calculated the area for me automatically. I also used microsoft excel as a program to calculate my values for z^n-1, using =COS(k*2*PI()/n) for a and =SIN(k*2*PI()/n) for b where z^n = a+bi (anyone else whos doing the IA should do this, it makes things alot less tedious) but i havent gotten to the second half of the IA yet.i've done the same thing as you and also got the same conclusion that as 'n' tends to infinity, the area tends to pii know that they didn't ask anything about the area but i was told that they appreciate any incentive from the students' side. Reply Link to post Share on other sites More sharing options...
The one you know Posted June 25, 2011 Report Share Posted June 25, 2011 Hey guy; i think most of you guys already finished the internal assessment for Maths; but i kinda started it now. i understand that we have to write it likr a report. how could you do that? i am always crap at starting things off,, any ideas for introduction? and also.. i've solved z^3-1=0. but i have to plot the roots on an argand diagram as well as a unit circle with centre origin.. how do i do that? and how could i draw a line segment from one root to another?? Help would be really appreciate it.. as i have not got any time!! thanks a lot!! Reply Link to post Share on other sites More sharing options...
dessskris Posted June 26, 2011 Report Share Posted June 26, 2011 Hey guy; i think most of you guys already finished the internal assessment for Maths; but i kinda started it now. i understand that we have to write it likr a report. how could you do that? i am always crap at starting things off,, any ideas for introduction? Have a good look at this --> http://www.ibsurvival.com/topic/12330-mathematics-portfolio-tips-for-hl-and-sl/ and also..i've solved z^3-1=0. but i have to plot the roots on an argand diagram as well as a unit circle with centre origin.. how do i do that? and how could i draw a line segment from one root to another?? Help would be really appreciate it.. as i have not got any time!! thanks a lot!! I suggest getting Autograph, a graphing software. it's not a freeware but there is a 30 days trial version available on the net. get it first, then I'll tell you the steps. otherwise it might be useless as you might not want to use that software haha Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 9, 2011 Report Share Posted July 9, 2011 My conjecture was that the roots of unity were evenly spaced out around a unit circle, since the lengths of the line segments seemed to be equal! I'm not sure if its the correct one! Any ideas on how to prove it? Reply Link to post Share on other sites More sharing options...
dessskris Posted July 10, 2011 Report Share Posted July 10, 2011 your conjecture should be something in form of an equation. not a simple statement like that.you need to find the equation for the length of the line segment in terms of n. Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 10, 2011 Report Share Posted July 10, 2011 Oh crap, I did find the lengths for each of them, I'm sure it has something to do with 2pi and the n being the number of sides on the polygon..2pi/n being the circle divided by the number of sides on polygon! but I just can't seem to get it! Reply Link to post Share on other sites More sharing options...
dessskris Posted July 10, 2011 Report Share Posted July 10, 2011 try to find it generally in terms of n. Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 10, 2011 Report Share Posted July 10, 2011 Yeah..thats what I'm trying to do, I'll get it eventually! Its not too bad! I did the patterns of linear equations portfolio, my tutor didn't accept it can't believe it, it is for assessment in 2012, and I did it well I'm sure! Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 14, 2011 Report Share Posted July 14, 2011 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?????? Reply Link to post Share on other sites More sharing options...
dessskris Posted July 16, 2011 Report Share Posted July 16, 2011 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??????I think they are asking you to generalise the solutions to z^n=i ONLY. so it's the z in terms of n. Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted July 20, 2011 Report Share Posted July 20, 2011 Oh wow thats easy peesy thanks for ur help, I appreciate it ! Reply Link to post Share on other sites More sharing options...
K.Hosny.M Posted July 22, 2011 Report Share Posted July 22, 2011 guys please i need helpi am stuck at bullet number 7,8* Use graphing software to test your conjecture for some more values of n and makemodifications to your conjecture if necessary.* Prove your conjecture.and in part Bin the last two bulletplease anyone tell me how to generalize ????what do they mean by this ?and what happens when |a+bi| not equal 1 ??please help guysthanks Reply Link to post Share on other sites More sharing options...
luve Posted July 24, 2011 Report Share Posted July 24, 2011 Hey Aren't the HL portfolio task the following Only??! : Task 1: How many pieces patterns within systems of linear equations Task 2: Running with Angie and Buddy Modelling a functional building Reply Link to post Share on other sites More sharing options...
luve Posted July 24, 2011 Report Share Posted July 24, 2011 Is this portfolio for Ib students doing their final exams in May 2012, or 2013 ?????would highly appreciate an answer... Reply Link to post Share on other sites More sharing options...
dessskris Posted July 24, 2011 Report Share Posted July 24, 2011 Hey Aren't the HL portfolio task the following Only??! :Task 1:How many piecespatterns within systems of linear equationsTask 2:Running with Angie and BuddyModelling a functional buildingthe tasks that you listed are meant for 2011 and 2012 students.there are new tasks for 2012 and 2013 students:type 1* Shadow functions* Patterns from complex numberstype 2* The dice game* Filling up the petrol tankif you're a 2012 students, you can choose from the 11/12 tasks and from the 12/13 tasks. Reply Link to post Share on other sites More sharing options...
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