Guest Posted December 17, 2014 Report Share Posted December 17, 2014 Please help.... find the sum of (Ui * Vi) until i = 10 , which means i = 1,2,3,4,....10. Ui = -3+4i Vi = 12-3i I know the answer is -1845 but i don't have a clue where it came from. Please suggest... Reply Link to post Share on other sites More sharing options...
ctrls Posted December 17, 2014 Report Share Posted December 17, 2014 You're trying to find the sum, One way that comes to mind is to note the linearity property of summation, namely that, Where are constants. Calculating the sum of the sequence isn't exactly easy unless you know a specific identity to do it (which isn't in the IB syllabus), but that does simplify the calculation a fair bit (though it is still fairly messy, none of the multiplications are particularly nice). I'm not too sure how else you can easily sum this without a calculator, where did you get this question from? 2 Reply Link to post Share on other sites More sharing options...
Vioh Posted December 17, 2014 Report Share Posted December 17, 2014 You're trying to find the sum, One way that comes to mind is to note the linearity property of summation, namely that, Where are constants. Calculating the sum of the sequence isn't exactly easy unless you know a specific identity to do it (which isn't in the IB syllabus), but that does simplify the calculation a fair bit (though it is still fairly messy, none of the multiplications are particularly nice). I'm not too sure how else you can easily sum this without a calculator, where did you get this question from? This is exactly what I thought as well. If this question was in indeed IB's, then it would probably be a calculator question. On the other hand though, the sum of the squares can be simplified by using this identity (from http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm): ; in other words With this identity, the calculations can be easily done by hand; but of course this is not in the syllabus, so don't even bother. Use your Ti-84 Reply Link to post Share on other sites More sharing options...
Guest Aniruddh Posted December 17, 2014 Report Share Posted December 17, 2014 (edited) I have attached my solution. Regards Aniruddh Edited December 17, 2014 by Aniruddh Reply Link to post Share on other sites More sharing options...
Guest Posted December 17, 2014 Report Share Posted December 17, 2014 (edited) I have attached my solution. Regards Aniruddh You're trying to find the sum, One way that comes to mind is to note the linearity property of summation, namely that, Where are constants. Calculating the sum of the sequence isn't exactly easy unless you know a specific identity to do it (which isn't in the IB syllabus), but that does simplify the calculation a fair bit (though it is still fairly messy, none of the multiplications are particularly nice). I'm not too sure how else you can easily sum this without a calculator, where did you get this question from? This is exactly what I thought as well. If this question was in indeed IB's, then it would probably be a calculator question. On the other hand though, the sum of the squares can be simplified by using this identity (from http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm): ; in other words With this identity, the calculations can be easily done by hand; but of course this is not in the syllabus, so don't even bother. Use your Ti-84 You're trying to find the sum, One way that comes to mind is to note the linearity property of summation, namely that, Where are constants. Calculating the sum of the sequence isn't exactly easy unless you know a specific identity to do it (which isn't in the IB syllabus), but that does simplify the calculation a fair bit (though it is still fairly messy, none of the multiplications are particularly nice). I'm not too sure how else you can easily sum this without a calculator, where did you get this question from? OMG I am so glad that it is not in the IB syllabus . I locked myself in my room for 2 hours , trying to solve that stupid question. Now i am happy. By the way i got it from my IBID maths HL book .... weird weird But thank you sooooo much. Edited December 17, 2014 by Guest Reply Link to post Share on other sites More sharing options...
Guest Aniruddh Posted December 17, 2014 Report Share Posted December 17, 2014 No one in my class got it either but then our math teacher taught us how to do it. Reply Link to post Share on other sites More sharing options...
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