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#1 |
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FFR Player
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pi = ln(-e)-1/sqrt(-1)
The original equation is ln(-e) = 1 + (pi)i I just isolated pi. |
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#2 |
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Retired BOSS
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Yes. I know why.
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RIP |
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#3 |
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FFR Hall of Fame
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You're just rearranging Euler's identity with some added terms:
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#4 |
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Resident Penguin
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I just typed the same thing as ap but vb swallowed it...
and that identity comes from some Calc II nonsense I believe, with series and whatnot. |
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#5 |
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Anxiety monster
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damn smart ****s
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#6 | |
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Quote:
![]() It's generally known as Euler's formula. I think you can prove it with Calc II series, but the first application I've seen of it was solving 2nd order linear ODEs that have complex conjugates as answers.
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#7 | ||
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Oh hey this topic came up almost a year ago.
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#8 |
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Super Scooter Happy
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Shame on me for not being familiar with that too.
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I watched clouds awobbly from the floor o' that kayak. Souls cross ages like clouds cross skies, an' tho' a cloud's shape nor hue nor size don't stay the same, it's still a cloud an' so is a soul. Who can say where the cloud's blowed from or who the soul'll be 'morrow? Only Sonmi the east an' the west an' the compass an' the atlas, yay, only the atlas o' clouds. |
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#9 |
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FFR Player
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this all came out when I was taking an Algebra II test, and trying to find one of the ever prevalent patterns. I plugged in ln(-e), and realized that the calculator spat out pi(i)+1, and I was like, "what the hell", and I tried to isolate e, but lacked the mad skills to do so. I know from where e is derived but never knew why.
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#10 |
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is against custom titles
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They didn't teach you what the log function looked like in Algebra II? What the hell were you trying to do taking the natural log of a negative number?
--Guido http://andy.mikee385.com |
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#11 | |
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FFR Hall of Fame
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#12 |
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is against custom titles
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Funny, as I'm taking Functions of Complex Variables right now. Very cute.
Note how he's in algebra II. Also note that I said natural log. I am well aware that there are an infinite number of solutions to log(-x) for any x, and how log and Log mean very different things. --Guido http://andy.mikee385.com |
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#13 |
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FFR Hall of Fame
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I definitely did complex logarithms in my algebra II class.
Although I didn't see them again until differential equations
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#14 |
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Above and Beyond
Join Date: Nov 2005
Location: Toronto
Posts: 368
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HOLY CRAP!!! aperson u should get a new section for aperson's insanly hard questions becasue everyone under 18 or so has no ****ing clue wtf ur saying but ppl like it. this is because urs are mostly harder
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#15 | |
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FFR Hall of Fame
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#17 |
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is against custom titles
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No, I'm pretty sure studying complex algebra in algebra II isn't a normal thing.
All we ever did was know a little about complex roots of polynomials. We never got into anything in the real-complex plane, branch cutting, or anything like that. --Guido http://andy.mikee385.com |
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#18 | |
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Now fµck off. Now that it's out there no one cares. |
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#19 |
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FFR Player
Join Date: Jan 2006
Posts: 269
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I'm probably not noticing something, but aren't you not allowed to rearrange alternating series?
-fs |
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#20 |
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is against custom titles
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What exactly do you mean by rearranging? The terms are all just added, if that's what you're meaning...
--Guido http://andy.mikee385.com |
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