inb4/sci/ is trolled again.

But I would seriously like an answer to this and why.

4th root of -1

>>609286
What's that in the form of a+bi?

−(−i2)2

+-(1+i)/sqrt(2)

(-1±i)/SQR(2)

i^(1/2) which becomes

e^(i*pi/2)*(1/2) which becomes

e^(i*(pi/4)), there are 3 other possible answers, maybe someone has already posted them..

That wasn't very lulzy.

>>609334

other solutions are -e^(i*(pi/4)) and i*e^(i*(3pi/4)) and -i*e^(i*(3pi/4))

>Report submitted! This window will close in 5 seconds...

>>609347
Despite being a troll thread, this is one of the few threads that actually has to do with science or math that I've seen in a while.

>>609347
No need to run. It's just math.

>>609045

wut?

i^.5

>>609334
It's a square root, thus there are only 2 solutions (see fundamental theorem of algebra).

>>609371

it's a square root of a square root

now use your precious fundemental theorem of algebra again

>>609374
i isn't the unique square root of any number. sqrt(-1) is nice to introduce i to highschool kids, but that's about it.

>>609374
so? 3 is a square root of 9. that doesn't mean that there's only one square root of 3.

>>609398

so what you're saying is.. x^4+1=0 has 2 solutions?

>>609410

It has 4 solutions

So why does sqrt(i) have only 2 solutions, genuine question here.

>>609380
>thinks getting responses means trolling
lol

-1

>>609442
"Square" stands for 2. 2 solutions.
z4=−1 uses a power of 4. Guess how many solutions.

>>609442
because c^z, for some complex number c and integer z, has exactly |z| solutions, some real, some complex

>>609454

so what you are saying is sqrt(sqrt(-1)) is not the same as sqrt(i)?

in other words, i and sqrt(-1) are different?

OK you fucking morons. You fools obviously know dick about any of this. Heard of this much?

http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

Any non-constant polynomial of a single variable over the complex field has as many roots as its degree.

So the polynomial relation x^2+1=0 has TWO solutions. Similarly, x^n + 1 = 0 has n solutions. x^2 + i = 0 has TWO solutions, et cetera. Jesus Christ.

>>609473

nobody cares about your short temper for people who havent wikipedia'd as much stuff as you, if you look carefully people are actually asking questions (you know, that thing you do as a process of learning?), so either help them or go away.

Thank you.

>>609466
In function theory, you usually don't ditch one solution of a root like you do when using reals. Usually, all possible solutions are considered.
Actually, I'm not sure whether the complex root has a precise definition at all - as far as I know, writing a=sqrt(z) is just a sloppy version of saying "let z be the set of solutions of a^2=z".

>>609463
>has |z| solutions

wtf

>>609486

Bawwwww someone got their feelings hurt on 4chan.

>>609486
>implying you don't learn the statement of FTA in like 8th grade

loludumb

>>609503
typo; should've been "let sqrt(z) be the set of solutions of a^2=z".

>trollface
>checkmark (i)
>+20 replies

the samefag is strong in this thread

>>609442
Write out all 4 solutions to x^4 = -1. Two of them will square to i, and two will square to -i. There's your answer.

>>609505has |z| solutions

eg. x^-4 has 4 solutions

>>609534

... do you even know wtf |z| means?

>>609512
>>609507
>>609473

Samefag, you've been asked once already, help out or fuck off back to /b/

Well, since this is a "troll" thread, can I ask something itt completely unrelated to math or science that I've wanted to know for a while? I was just wondering how to post a message here with red text and how to make one of those spoiler boxes (the ones where you have to hover your mouse over it to read what's inside). I've seen it done here before and was just curious as to how it was done. Could someone please help. I won't do it here of course; perhaps I'll test it in /b/.

btw I already know how to triforce; so if either of the things I inquired about require unicode, I've had previous experience. *shrug*

>>609562

I'm the only one who gave a concrete answer. I still don't know what you are not understanding.

>>609583

Posting a link from wikipedia about the fundemental theorem of algebra does not answer the question

>>609466


The only helpful people in here were Josef and some other non-nob head anons.

>>609608

I posted the Wikipedia page in lieu of actually writing out the statement of the theorem. This conversation seems to be revolving around the confusion over how many nth-roots there are of a certain complex number. The FTA answers this question precisely: there are n complex roots of any complex number. Therefore, the troll's original question can be stated differently: what are the solutions of x^{2} = i over the complex field? The answers are exp{i*\pi/4} and exp{i\5pi/4}.

>>609608

Since we have found two roots of the polynomial relation x^2 = i, the FTA guarantees that these two are unique.

just visualize it on the complex plane. It would have 2 solutions, the first at 45 degrees and the second at 225 degrees. In other words it would be something like.

cos(45) + i sin (45)
and
cos(225) + i sin(225)

Alternatively you can write it in polar coordinates like this.

e^((i)(pi/2))
and
e^((i)(5pi/4))

It can also be represented in matrix coordinate form if you want to.

>>609642
Bawwwww someone got their feelings hurt on 4chan.

>>609268


godamn it 40+ replies.