I took an algebra test today and the first part to solving the problem was to find the square root. I came across -100, at first I thought it was -10, then i realized that -10 squared is 100 and 10 squared is also 100. I entered it into the TI-83 and got a syntax error. I used -10 cause I didnt know what else to do. Anyone have some thoughts on this?

[quote author=LW-Falcon link=board=36;threadid=6684;start=0#msg58892 date=1083905542]
I took an algebra test today and the first part to solving the problem was to find the square root. I came across -100, at first I thought it was -10, then i realized that -10 squared is 100 and 10 squared is also 100. I entered it into the TI-83 and got a syntax error. I used -10 cause I didnt know what else to do. Anyone have some thoughts on this?
[/quote]

sqrt(-100) = 10i

If you're working in reals, -100 has no square root and you reached it either through a miscalculation, or because there's actually no solution to the equation you were trying to solve (example: x^2 + 100 = 0).

In complex numbers, every number has a square root (and any n'th root as well). The square root of -100 is 10i where i is an imaginary number defined as i = sqrt(-1).

Is i necessary for -100 to have a square root?

Bah, my teacher never taught me that, thats a 98% so far. :(

[quote author=Adron link=board=36;threadid=6684;start=0#msg58935 date=1083948662]
Is i necessary for -100 to have a square root?
[/quote]No, you can use other methods like Eisenstein integers or quaternions, but complex numbers are much more common...

(You're probably thinking of something evil that I'm going to fall for. :()

I was thinking of a minor evil. Just that of sqrt(-100) vs sqrt(pi) or any other number that we can't evaluate numerically, yet don't have a special symbolic constant for.

Sometimes I hear people saying that by defining i as sqrt(-1), sqrt(-100) becomes valid, but in my opinion that's not it. All you have to do is say that roots of negative numbers are valid. And you have to say that either way. Whether we have a name for it or not doesn't matter at all.

Just a matter of how you think about it.

Oh, yes. That's what I said, you don't have a solution when you're working in reals, but in complex numbers you do ("every number has a square root"). In addition to that, assuming the common definition of sqrt(-1) as i, the square root of -100 evaluates to be 10i.

Yes... It was meant more as a question for everyone else to think about, not specifically to you ;)

[quote author=LW-Falcon link=board=36;threadid=6684;start=0#msg58955 date=1083965782]
Bah, my teacher never taught me that, thats a 98% so far. :(
[/quote]

I didn't learn i until Algebra II/Trig (this year.) >:(

I didn't learn i until this year in Algebra II, so don't feel bad :P.

Your teacher lets you use TI-83's on your test? Damn, I wish I was that lucky. Oh well, I've only had 2 tests this whole year I haven't received 100% on.

[quote author=LW-Falcon link=board=36;threadid=6684;start=0#msg58955 date=1083965782]
Bah, my teacher never taught me that, thats a 98% so far. :(
[/quote]

We were taught early that the square root of a negative number is undefined, and that would have been the correct answer on the test (when I was in math). They didn't want us using imaginary numbers back then.

This is a bit off topic, but don't you guys just hate that complex numbers are called, "imaginary numbers?" I mean, technically, they're as real as any other number gets, unlike the name implies. I just finished my Euclidean Geometry course for my Freshman year, so I don't know much about i, except that it works the same way as ratios do (don't immediatly disreguard what I'm saying), such that 3/1 isn't technically 3, since 3 is 3 times greater than one, it can be expressed as the ratio 3 to 1, or the real number 3, as i can be expressed in the real form of [sqrt]-1. Correct me if I'm wrong, but just to reiterate, I hate that they are called imaginary, just because the name was, "stuck."

[quote author=Maddox link=board=36;threadid=6684;start=0#msg60888 date=1085015321]
Your teacher lets you use TI-83's on your test? Damn, I wish I was that lucky. Oh well, I've only had 2 tests this whole year I haven't received 100% on.
[/quote]

I'm in Pre-Calc this year and trust me when my teacher lets us use calculators, she makes the tests so difficult that it's impossible to solve any single problem without it. So I'd rather have problems that you could solve in your head such as the sqrt(-100) rather than having logarithms etc.

[quote author=aDDicT link=board=36;threadid=6684;start=0#msg61806 date=1085514142]
I'm in Pre-Calc this year and trust me when my teacher lets us use calculators, she makes the tests so difficult that it's impossible to solve any single problem without it. So I'd rather have problems that you could solve in your head such as the sqrt(-100) rather than having logarithms etc.
[/quote]

I think you can probably solve problems fine without a calculator, you just can't give a numerical / decimal answer, but have to give exact answers.

[quote author=aDDicT link=board=36;threadid=6684;start=0#msg61806 date=1085514142]
I'm in Pre-Calc this year and trust me when my teacher lets us use calculators, she makes the tests so difficult that it's impossible to solve any single problem without it. So I'd rather have problems that you could solve in your head such as the sqrt(-100) rather than having logarithms etc.
[/quote]
That sounds really stupid. Math tests shouldn't contain many numbers, mostly letters. The reason they let you use calculators is because you don't need them at all, not to make them absolutely necessary by introducing annoying numbers.

[quote author=iago[yL] link=board=36;threadid=6684;start=0#msg60995 date=1085077570]
We were taught early that the square root of a negative number is undefined, and that would have been the correct answer on the test (when I was in math). They didn't want us using imaginary numbers back then.
[/quote]
Grade 11, they expect us to know them and use them.

[quote author=ITAKal89 link=board=36;threadid=6684;start=0#msg61253 date=1085263987]
This is a bit off topic, but don't you guys just hate that complex numbers are called, "imaginary numbers?"
[/quote]
I think it's like that cause "i" isn't a number?

But they're still no more imaginary than other numbers.

[quote author=ITAKal89 link=board=36;threadid=6684;start=15#msg61908 date=1085542123]
But they're still no more imaginary than other numbers.
[/quote]

I suppose the difference is that there aren't any normal tangible physical quantities that are measured in imaginary numbers...