Imaginary numbers

[Sayonara]

neo_maya said in post #71 :

Hey, I think there should be a sqrt sign in the smilies list - don't you think?

Use the ^superscript tags.

[JaKiri]

Sayonara³ said in post #76 :

Use the ^superscript tags.

 

I was going to find an image of a square root sign to demonstrate what she meant, but when searching google for square root, the first thing up was This, which is much more appealing as a smiley.

[neo_maya]

MrL_JaKiri said in post #75 :

Make a new thread

 

 

 

I already have.

 

Sayonara is a she !!!!!!!!!!!!!!??????????!!..........

[neo_maya]

No offence.

[JaKiri]

My fingers, they type of their own accord.

[Kedas]

MrL_JaKiri said in post #63 :

No.

 

That's equivilent to saying that -4 = 4, because SQRT(16) = 4

 

SQRT(16) = -4

 

Hence -4 = 4.

 

what ??

 

I start with -1=-1 and end with 1=-1 without making any obvious mathematical error.

 

BTW I know that 1=-1 is wrong but that's the point of the message.

 

with numbers:

2.2=4

sqrt(-4).sqrt(-4)=4

sqrt(-4.-4)=4

sqrt(16)=4

 

The difference is that no one claims that sqrt(-4)=2 but they do claim sqrt(-1)=i.

 

[Tom Mattson]

YT2095 said in post #56 :

and so, if you calculate the sqr rt of -1, what is the answer?

 

The answer is 'i'.

 

in one post you say it`s not a number like "35" and in another you say is IS a number? Kinda WELL LOST here!

 

OK, how about this:

 

'i' is not an element of Z, as 35 is.

'i' is an element of C, as 35 also is.

[Tom Mattson]

Kedas said in post #62 :

i^2=-1 not the same as i=sqrt(-1)

 

You're right: i²=-1 contains more information than does i=sqrt(-1). -1 (like all numbers) actually has two square roots: +i and -i.

 

There is a funny 'prove' about it that says that -1=1

 

i.i=-1

sqrt(-1).sqrt(-1)=-1

sqrt(-1.-1)=-1

sqrt(1)=-1

1=-1

 

The part in red is where the mistake was made. MrL Jakiri's comment was right. I can do the exact same thing with real numbers.

 

2*(-2)=-4

sqrt(4)*sqrt(4)=-4

sqrt(16)=-4

4=-4

 

Ta-Daaaa!

[Kedas]

yeah, it's a funny thing to keep people busy

 

I only wanted to point out the difference between the two with some proof.

Not to start a debate about the comparison with real numbers.