complex numbers

Find the roots of the equation (z+1)^3 = 1, in the form x+iy.

gogogo

>>33
Simple question here: If you asked for a real number, and I responded "5/2", would you complain?

(Hint: it's one of those damned-if-you-do-damned-if-you-don't situations.)

>>41
Of course I wouldn't complain.  "5/2" is a perfectly acceptible way of writing a real number.

By the way, how is it "damned if I do?"  I understand "damned-if-I-don't" because it's totally acceptible.  How does the first part play out?

>>33

Catholics DO suck. You'd have to be a true IDORT to believe that shit.

>>41
this is more analogous to being asked to give an integer and responding 42/7.

people might wonder why you didnt reduce it and format it the standard way, but no one really cares.

>>42
Because it's inconsistent to accept a ratio of real numbers as a real number when you obviously will not accept a ratio of complex numbers (indeed, a complex number divided by a real number, which is even nicer) as a complex number. Either you are incapable of going from (a+bi)/c -> a/c + i*b/c, or you are attempting to force your slow-witted high school teacher's idiotic grading policies on people who know better. In the former case, you're a fucking moron and you should gb2/middleschool/. In the latter case, you're a different kind of fucking moron, and you should kill yourself.

>>44
I would say that 5/2 (as a real number) and (a+bi)/c (as a complex number) are roughly equivalent concepts. Since complex numbers and real numbers both are fields, there is no worry about the division operation (provided c is nonzero). In the integers I'd be hesitant to give an answer in the form a/b even assuming a was a multiple of b, as division is not defined for all pairs of integers. I'm not saying 42/7 would be unacceptable, just that it would be considerably more odd than (a+bi)/c.

>>45
(a+bi)/c is a ratio of complex-to-real.  real-to-real is okay.  complex-to-real takes from two different fields.  A field only has closure for an operation if you can get back to the same field through the operation.  as complex and real are different fields, division isn't necessarily closed, mirite?

that's why (a+bi)/c is incorrect and a/c+i*b/c is correct.  the latter only has real-to-real ratios (one of them being multiplied by i), while the former has a complex over real which, like i said, takes from two different fields.

>>46
reals are in complex, complex to real is complex to complex.  now its a ratio of things from the same field.

>>46
So you read the word "field" somewhere on Wikipedia and decided to pull that out of your ass, did you?

>>48

LOL, that's true for most of replies in /sci/

>>46
How about Reel-to-Reel?  I Like to Move It Move It, I Like to Move It Move It, I Like to Move It Move It, bomp bomp bomp bum bum bomp bomp bomp bomp I Like to Move It Move It

Stop.



Hammertime.

>>48
no, but i've taken classes in abstract algebra, group theory, and two linear algebra courses.
are you suggesting that a real number is not a complex number?  >>46 was insinuating that a ratio of complex to real numbers may not be meaningful as a complex number because the numbers came from different fields.  if you're not a retard, you probably already know that the reals are a subset of the complex numbers, so any real number is a complex number.  so, while he would have a point if we were talking about whether or not the ratio made sense in the reals; we weren't.

>>52
I'm somewhat lost here. You seem to be telling >>48 that you know what you're talking about while simultaneously explaining why >>46 was wrong, despite the fact that >>48 was insulting >>46.

>>53
that's because i can't read and i thought >>48 was directed at >>47

woopzlol.

>>47
Then reduce for me the following:

(4+6i)/(8+10i)

Surely, this can be put into some kind of a+bi form, without remaining a quotient, right?

>>55
(23/41) + (2/41)i

>>55
relatedly
(a+bi)/(c+di) = [(ac+bd)/(cc+dd)] + [(bc-ad)/(cc+dd)]*i

this is defined as long as at least one of c or d are nonzero.  i.e. as long as the modulus of c+di is nonzero.

whats the fuckin difference between (a + bi)/c and a/c + bi/c ... the first is even better if you ask me

>>56
is (23+2i)/41 also an acceptible way to write that answer based only on this thread?

also, >>57,
is it also accpetible to write:
(a+bi)/(c+di) = [(ac+bd)+(bc-ad)i]/(cc+dd)

again based only on this thread?

>>59
i'm both 56 and 57.  but yeah, those are also an acceptable way to write both.  i don't know what 'based only on this thread' has to do with it.  if you have a working knowledge of fractions (ie, you didnt fail algebra), you should see that they are equivalent.