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Imaginary numbers


eric

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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.

 

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  • 4 weeks later...
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.

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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!

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