Maths question

[skeliton112]

I realise this isn't really a maths forum but its the only website I have an account with atm so I thought that I might as well post it here.

the other day when I was playing around with imaginary numbers I decided to find out what the quad root of -1. I came up with (i+1)/root(2).

i=i^5

root(i) = root(i^4)*root(i)
root(i) = i^2*root(i)
therefore root(i)=-root(i)

This is obviously incorrect and if you follow through you can show that -root(2) = root(2).

I was wondering if anyone knew where the mistake was in my reasoning as it has been bugging me all day.

 

[SckizoBoy]

Well... your mistake is believing a conventional operator can be applied to an imaginary expression that has no real components... *shrug*

EDIT - just read that back... how wrong it is... *gestures along* move on folks...

 

[Smertnik]

Even roots can be both positive and negative. The one in question (\sqrt{i^4}) is obviously negative.

 

[ClockworkPenguin]

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).

 

[Smertnik]

Is it now? root(i^4) = root(1)

Yes? The square root of 1 can be both 1 and -1. In this case only -1 offers the correct result.

 

[RADIALTHRONE1]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

 

[The Almighty Aardvark]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

 

[Jimmy T. Malice]

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

 

[RADIALTHRONE1]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

Ok, you lost me at... Well you never actually had me.
I'm just going to stop trying before my head explodes.

Wait! I have an idea!

root(-1) = i
0

Fuuu

 

[The Almighty Aardvark]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

Ok, you lost me at... Well you never actually had me.
I'm just going to stop trying before my head explodes.

Wait! I have an idea!

root(-1) = i
0

Fuuu

I'll take another shot at explaining for the potentially amusing event of your head exploding.

You know how if you multiply two roots together it acts like normal multiplication? Occasionally you'll find yourself in a situation where you need to deal with the square root of a negative number. A way to work around this is instead of dealing with root(-36) you can change it to root(-1)*root(36) and then simplify it by changing root(-1) to i and root(36) to 6. So the answer to root(-36) would be 6i.

This doesn't come up often in regular math but they were brought up in either (or both) linear algebra and calculus. Actually, I'm almost positive I used them in linear algebra.

 

[DoPo]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

Ok, you lost me at... Well you never actually had me.
I'm just going to stop trying before my head explodes.

Wait! I have an idea!

root(-1) = i
0

Fuuu

I'll take another shot at explaining for the potentially amusing event of your head exploding.

You know how if you multiply two roots together it acts like normal multiplication? Occasionally you'll find yourself in a situation where you need to deal with the square root of a negative number. A way to work around this is instead of dealing with root(-36) you can change it to root(-1)*root(36) and then simplify it by changing root(-1) to i and root(36) to 6. So the answer to root(-36) would be 6i.

This doesn't come up often in regular math but they were brought up in either (or both) linear algebra and calculus. Actually, I'm almost positive I used them in linear algebra.

And now I want to see a live feed of him reading that explanation. Well, not that it's going to happen. I'll settle for photos.

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

 

[ClockworkPenguin]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

Ok, you lost me at... Well you never actually had me.
I'm just going to stop trying before my head explodes.

Wait! I have an idea!

root(-1) = i
0

Fuuu

I'll take another shot at explaining for the potentially amusing event of your head exploding.

You know how if you multiply two roots together it acts like normal multiplication? Occasionally you'll find yourself in a situation where you need to deal with the square root of a negative number. A way to work around this is instead of dealing with root(-36) you can change it to root(-1)*root(36) and then simplify it by changing root(-1) to i and root(36) to 6. So the answer to root(-36) would be 6i.

This doesn't come up often in regular math but they were brought up in either (or both) linear algebra and calculus. Actually, I'm almost positive I used them in linear algebra.

Just like to add that they aren't just a 'pure maths' thing. Some real world things can have imaginary values. For example, the impedance of a capacitor is given by 1/(iCw)where w is the frequency of the ac voltage and C is the capacitance of the capacitor.

 

[The Almighty Aardvark]

And now I want to see a live feed of him reading that explanation. Well, not that it's going to happen. I'll settle for photos.

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

Haha, the irony of saying that i isn't a complex number is hilarious if unintentional. It's the BASIS of complex numbers

I completely agree with the statement it isn't that difficult to understand, but your exact choice of words are amusing

Just like to add that they aren't just a 'pure maths' thing. Some real world things can have imaginary values. For example, the impedance of a capacitor is given by 1/(iCw)where w is the frequency of the ac voltage and C is the capacitance of the capacitor.

I'm fairly new to them, so all I've seen them in so far are the two subjects I mentioned. I don't remember mention of that in high school physics though, is that covered in university level classes?

 

[DoPo]

And now I want to see a live feed of him reading that explanation. Well, not that it's going to happen. I'll settle for photos.

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

Haha, the irony of saying that i isn't a complex number is hilarious if unintentional. It's the BASIS of complex numbers

Yes, 'twas the joke. Even though it's a complex number, it's not actually complex to understand.

 

[RADIALTHRONE1]

Looking at this makes my head hurt.

What is this, Calculus or something? I just started Algebra 2, and i can't make heads or tales of it.
[sub]Or i'm just to lazy to try[/sub]

i is an imaginary number where root(-1) = i

Ok, you lost me at... Well you never actually had me.
I'm just going to stop trying before my head explodes.

Wait! I have an idea!

root(-1) = i
0

Fuuu

I'll take another shot at explaining for the potentially amusing event of your head exploding.

You know how if you multiply two roots together it acts like normal multiplication? Occasionally you'll find yourself in a situation where you need to deal with the square root of a negative number. A way to work around this is instead of dealing with root(-36) you can change it to root(-1)*root(36) and then simplify it by changing root(-1) to i and root(36) to 6. So the answer to root(-36) would be 6i.

This doesn't come up often in regular math but they were brought up in either (or both) linear algebra and calculus. Actually, I'm almost positive I used them in linear algebra.

And now I want to see a live feed of him reading that explanation. Well, not that it's going to happen. I'll settle for photos.

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

Spoiler: I believe i looked kinda looked like this-

Although i kinda get waht Almighty Aardvark is saying though.
Your breaking root(-36) into two parts, simplifying one part and substituting the other part for a variable.

[sub]I think.[/sub]

 

[Lunar Templar]

o.0?!

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

 

[burningdragoon]

Hey! math should probably go into the <code></code> tags. Reading equations without nice, even spacing makes you go blind is annoying.

 

[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?

 

[Evil Smurf]

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.