Maths question

[skeliton112]

I think the fourth root of -1 is still i.

No that doesnt work, because the fourth root of i has to equal i squared when squared. I got to my answer by using basic math.

(ix+y)^2=y^2-x^2+2ixy therefore

x-y=0
xy=1/2=x^2
x=(+/-)root(1/2)=1/(+/-)root(2)

so (i/(+/-)root(2)+1/(+/-)root(2))^2=i

root(i)=(+/-)(1+i)/(+/-)root(2)

 

[Rabid Toilet]

The mistake comes from the fact that you are trying to take only the positive root of both sides of the equation, which you can't do. When you square root each side, you're taking the positive and negative roots.

 

[tensorproduct]

Although, i isn't that complex, really. Just a number. That doesn't exist, hence "imaginary". Nothing too bad.

i exists every bit as much as -1, or pi. Just because it's marginally harder to think about doesn't make it less real (though it's not Real).

 

[ClockworkPenguin]

I think the fourth root of -1 is still i.

No that doesnt work, because the fourth root of i has to equal i squared when squared. I got to my answer by using basic math.

(ix+y)^2=y^2-x^2+2ixy therefore

x-y=0
xy=1/2=x^2
x=(+/-)root(1/2)=1/(+/-)root(2)

so (i/(+/-)root(2)+1/(+/-)root(2))^2=i

root(i)=(+/-)(1+i)/(+/-)root(2)

yeah, but each plus/minus choice is independent of the others, so whichever way round you write them, you'll get 2^n equations (n being the number of plus/minus choices in your equation, in this case 2) of which half will be correct. Discard the other half.

 

[Zantos]

you make a simple mistake here.

to make an analogy
sqrt(4)=2
sqrt(4)=-2

therefore -2 = 2. this is incorrect, the solution to this paradox is that numbers have multiple roots.

If you wanted to find the quad root of -1, you should expect 4 answers (some of the answers may happen to be identical).

Thanks. I realised after going to bed that I forgot to use the plus-minus symbol when rooting, which would change it to:

plus-minus root(i)=minus-plus root(i), which is still incorrect isn't it?

Why would that be incorrect? The order in which you say plus or minus isn't important, what's important is you've got two solutions where one's the negative of the other. There are four possibilities coming from that combination,

+root(i) = -root(i)
+root(i) = +root(i)
-root(i) = -root(i)
-root(i) = +root(i)

In which we can see that two are true trivially, the other two are discarded as false.

 

[skeliton112]

you make a simple mistake here.

to make an analogy
sqrt(4)=2
sqrt(4)=-2

therefore -2 = 2. this is incorrect, the solution to this paradox is that numbers have multiple roots.

If you wanted to find the quad root of -1, you should expect 4 answers (some of the answers may happen to be identical).

Thanks. I realised after going to bed that I forgot to use the plus-minus symbol when rooting, which would change it to:

plus-minus root(i)=minus-plus root(i), which is still incorrect isn't it?

Why would that be incorrect? The order in which you say plus or minus isn't important, what's important is you've got two solutions where one's the negative of the other. There are four possibilities coming from that combination,

+root(i) = -root(i)
+root(i) = +root(i)
-root(i) = -root(i)
-root(i) = +root(i)

In which we can see that two are true trivially, the other two are discarded as false.

I just reread and realised the minus-plus thing is invalid as in this case the plus-minus signs are not all alike. The order of the plus and the minus only matters when all plus minus symbols must be the same and in that case the minus plus is the opposite sign.

Anyway thankyou for your help that was annoying me.

 

[Lunar Templar]

o.0?!

what the hell are letters doing in your math problem .....

algebra bro Maths like this makes my brain hurt, I just use my calculator.

algebra o.o;;;; yeah .... i suck so hard at algebra its not even remotely funny

 

[Mr F.]

I thought this was going to be another one of those "Snipe the nerds with a simple equation that causes anger" thing. You know, along the same lines as "I just asked you a logic question which was not a logic question, simply an excercise used in making people think in an abstract fashion".

Yeah, I thought this was a troll thread.

Then you had to go and make my BRAIN HURT.

OT: Wait, what? I guess its a good thing I am a sociology major.

I wish I knew how to link images.

http://xkcd.com/1052/