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| − | For problem 9.3, how detailed should our explanation be? Is a mathematical proof required along with our reasoning in words? --[[User:Ysuo| | + | For problem 9.3, how detailed should our explanation be? Is a mathematical proof required along with our reasoning in words? --[[User:Ysuo|Yu Suo]] |
| − | Write out the real and imaginary parts for <math>\log(a_1a_2)</math> then choose the principal branch of log and add <math>2n\pi</math> to get all the possible branch choices. Next do the same for <math>\log(a_1)+\log(a_2)</math> only using two different variables (one for each number) for the possible branches. Adding the results of the two logs together should give a relation between all the variables. Hope this helps --[[User:Rgilhamw| | + | Write out the real and imaginary parts for <math>\log(a_1a_2)</math> then choose the principal branch of log and add <math>2n\pi</math> to get all the possible branch choices. Next do the same for <math>\log(a_1)+\log(a_2)</math> only using two different variables (one for each number) for the possible branches. Adding the results of the two logs together should give a relation between all the variables. Hope this helps --[[User:Rgilhamw|Robert Gilham-Westerman]] 18:47, 4 October 2009 (UTC) |
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Also Prof Bell, If you do read this could you please post the lecture notes from last class online. | Also Prof Bell, If you do read this could you please post the lecture notes from last class online. | ||
| − | Thanks --[[User:Kfernan| | + | Thanks --[[User:Kfernan|Kevin Fernandes]] 20:12, 4 October 2009 (UTC) |
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| + | Kevin, those arguments can be off by a multiple of <math>2\pi n</math> where n is an integer. Robert Gilham-Westerman has the right idea above. | ||
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| + | The notes are now posted. Sorry about that. --[[User:Bell|Steve Bell]] 21:41, 4 October 2009 (UTC) | ||
Latest revision as of 16:41, 4 October 2009
Homework 5
For problem 9.3, how detailed should our explanation be? Is a mathematical proof required along with our reasoning in words? --Yu Suo
Write out the real and imaginary parts for $ \log(a_1a_2) $ then choose the principal branch of log and add $ 2n\pi $ to get all the possible branch choices. Next do the same for $ \log(a_1)+\log(a_2) $ only using two different variables (one for each number) for the possible branches. Adding the results of the two logs together should give a relation between all the variables. Hope this helps --Robert Gilham-Westerman 18:47, 4 October 2009 (UTC)
So for 9.3 is it enough just to say $ arg(a1*a2)=arg(a1)+arg(a2) $ ??
Also Prof Bell, If you do read this could you please post the lecture notes from last class online.
Thanks --Kevin Fernandes 20:12, 4 October 2009 (UTC)
Kevin, those arguments can be off by a multiple of $ 2\pi n $ where n is an integer. Robert Gilham-Westerman has the right idea above.
The notes are now posted. Sorry about that. --Steve Bell 21:41, 4 October 2009 (UTC)
