sprintdominator Posted April 2, 2011 Report Share Posted April 2, 2011 Hey there, has any one gotten a mathematics hl type 1 portfolio on roots of unity, complex numbers? Reply Link to post Share on other sites More sharing options...
sheldonxp Posted April 7, 2011 Report Share Posted April 7, 2011 Yes I'm doing that, but I can't figure out how to prove the conjecture. Any ideas? Reply Link to post Share on other sites More sharing options...
dessskris Posted April 9, 2011 Report Share Posted April 9, 2011 is this the newest task?? (for 2013)can I have a PDF of it? or just scan the task paper.. I can try to help you guys Reply Link to post Share on other sites More sharing options...
DDuino Posted April 26, 2011 Report Share Posted April 26, 2011 Hello Guys...i have got to start my type one maths HL...is anybody having it for complex numbers?if yes let me know how are you doing-finding it. Reply Link to post Share on other sites More sharing options...
DDuino Posted April 27, 2011 Report Share Posted April 27, 2011 yeah i am struggling as well with it...i dont know as well...any ideas out from it???thanks guys... Reply Link to post Share on other sites More sharing options...
Wide Eyed Wanderer Posted May 2, 2011 Report Share Posted May 2, 2011 I did the one involving patterns in linear equations - but I can help you if you attach a pdf or something (: Reply Link to post Share on other sites More sharing options...
dessskris Posted May 2, 2011 Report Share Posted May 2, 2011 Reply Link to post Share on other sites More sharing options...
Kaiwen Posted May 11, 2011 Report Share Posted May 11, 2011 Oh my, mine is dued in 2 days and I still haven't decide on which to do yet ;P mainly because I don't even know what's the Moivre theorem Reply Link to post Share on other sites More sharing options...
dessskris Posted May 13, 2011 Report Share Posted May 13, 2011 (edited) the Moivre's Theorem:(rcisθ)n = rncis(nθ) Edited May 13, 2011 by dessskris Reply Link to post Share on other sites More sharing options...
Homira Rezai Posted May 31, 2011 Report Share Posted May 31, 2011 can someone please give me some hints on the following question... its HL maths A). use de moivre's theorem to obtain solution to the equation Z^3-1= 0. (I suck at maths HL) thank you, help will be appreciated! Reply Link to post Share on other sites More sharing options...
bomaha Posted June 1, 2011 Report Share Posted June 1, 2011 what does (generalize and prove your results for zn = a + bi, where /a+bi/ = 1) mean?It's bullet point no. 11.How can I generalize for it, because /a+bi/ = 1, means that zn = 1 or -1 or i or -i.Thanks in advance. I need help urgently. Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted June 1, 2011 Report Share Posted June 1, 2011 (edited) It's essentially just generalise the roots of unity. So what are the roots of unity for zn? If you've done the other parts, I can't see this being too hard. Proving it would be harder, but definitely possible.Remember that 1 = cis(2k pi) Edited June 1, 2011 by timtamboy63 Reply Link to post Share on other sites More sharing options...
bomaha Posted June 1, 2011 Report Share Posted June 1, 2011 (edited) It's essentially just generalise the roots of unity. So what are the roots of unity for zn? If you've done the other parts, I can't see this being too hard. Proving it would be harder, but definitely possible.Remember that 1 = cis(2k pi)The generalizing was easy, but I couldn't prove the conjecture for the distance between roots and the generalization for the roots of z^n = a+bi, where /a+bi/ = 1 How can you prove them?I heard that the conjecture can be proved analytically but I don't know what does analytically mean. Edited June 1, 2011 by bomaha Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted June 2, 2011 Report Share Posted June 2, 2011 (edited) I'll give it a go when I get some free time, but I suspect it might have something to do withcis(x) = eix Edited June 2, 2011 by timtamboy63 Reply Link to post Share on other sites More sharing options...
dessskris Posted June 2, 2011 Report Share Posted June 2, 2011 sorry for not replying to your PM. analytically means algebraically. you found the distance for every value of n using cos, right? now you do EXACTLY the same thing, just with the variable n instead of numbers. Reply Link to post Share on other sites More sharing options...
DDuino Posted June 3, 2011 Report Share Posted June 3, 2011 Bomaha,generalizing.. basically what you do you dont need to prove really...you just put down an example and you should be fine...think of the magnitude od a+bi when it equals 1...so that if you have done the other parts it should be very easy to come to the conclusion..the unit circle thing helps a lot for the answer...if you are still not ask again... 1 Reply Link to post Share on other sites More sharing options...
bomaha Posted June 3, 2011 Report Share Posted June 3, 2011 I have a question about pullet point no. 6 (Factorize zn-1 for n = 3, 4, and 5.)To what extent do I need to factorize? Reply Link to post Share on other sites More sharing options...
DDuino Posted June 3, 2011 Report Share Posted June 3, 2011 factorize always leaving a bracket (x-1)...so that one of the answers will always be 1...and see whether you can get it...this might help you to structure your conjecture Reply Link to post Share on other sites More sharing options...
dessskris Posted June 3, 2011 Report Share Posted June 3, 2011 you need to factorise it to get a multiplication of n linear functions.so when n=3 you need to get (z+a)(z+b)(z+c)=0 Reply Link to post Share on other sites More sharing options...
Gnick Wright Posted June 6, 2011 Report Share Posted June 6, 2011 Hi guys, I was wondering what sort of conjectures you could form from this? And how to prove such conjectures. My conjecture was that as N's value approaches infinity, the area of the polygon formed by the vectors between the points approaches pi. Thanks. Reply Link to post Share on other sites More sharing options...
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