What is the squre root of -1

[December]

Can somebody explain this...

I will use "sqrt" to denote square root...

In mathematics we say

sqrt(-1) = i This is a definition

Now i^2 = -1 (e.g. sqrt(4) = 2 ; therefore 2^2 = 4 )

i^2 = sqrt(-1)*sqrt(-1)

This can be written as

i^2 = sqrt((-1)*(-1)) (e.g. sqrt(2)*sqrt(2) = sqrt(2*2) )

so i^2 = sqrt(1) (as (-1)*(-1) = 1 )

i^2 = 1 (as sqrt(1) = 1 )

taking the square root of both sides

i = 1

But at the beginning i = sqrt(-1)

So sqrt(-1) = 1

 

[nagaya]

this is wrong bro


for the problem in the thread;
[sqrt(-1)]^2=-1 not +1,so it can't be done like this

 

[himalaka kalhara]

 

[December]

this is wrong bro
i^2 = 1
i = 1

this should be like this

i^2-1=0
(i-1)(i+1)=0
so i=1 or i=-1
by defintion i!=1
hence i=-1

But i=sqrt(-1)
so u hv proved dat
sqrt(-1) = (-1)

 

[Tom Riddle]

I think the mistake you are making is when you are saying

sqrt(-1)*sqrt(-1) = sqrt( (-1)*(-1) )

That rule must only apply to positive numbers (I haven't seen that it only applies to positive numbers in a book, but ALL the other steps that you have taken are correct)

I'll try to get a confirmation on the above.

 

[Tom Riddle]

Got confirmation. That rule doesn't apply to square roots of negative numbers.

http://mathforum.org/library/drmath/view/53873.html

 

[koondeGoda]

Can somebody explain this...

I will use "sqrt" to denote square root...

In mathematics we say

sqrt(-1) = i This is a definition

Now i^2 = -1 (e.g. sqrt(4) = 2 ; therefore 2^2 = 4 )

i^2 = sqrt(-1)*sqrt(-1)

This can be written as

i^2 = sqrt((-1)*(-1)) (e.g. sqrt(2)*sqrt(2) = sqrt(2*2) )

so i^2 = sqrt(1) (as (-1)*(-1) = 1 )

i^2 = 1 (as sqrt(1) = 1 )

taking the square root of both sides

i = 1

But at the beginning i = sqrt(-1)

So sqrt(-1) = 1

(-1) ^ 1/2 * (-1 )^ 1/2 = -1(1/2+1/2)= -1
hence
i^2 = -1
i = sqrt(-1)
back to the def

 

[nagaya]

But i=sqrt(-1)
so u hv proved dat
sqrt(-1) = (-1)

hari hari typing mistake dan haduwa

 

[Tom Riddle]

Further confirmation that what I said was correct. This article explains what is wrong in the EXACT SAME question.

http://en.wikipedia.org/wiki/Square_root

Look under the heading 'Principle square root of a complex number' -> Notes

 

[Tom Riddle]

this is wrong bro
i^2 = 1
i = 1

this should be like this

i^2-1=0
(i-1)(i+1)=0
so i=1 or i=srqt(-1)
by defintion i!=1
hence i=sqrt(-1)

should be i=1 or i=-1 neda machang? eka paaratama sqrt(-1) danna behene?

 

[reshadie]

Can somebody explain this...

I will use "sqrt" to denote square root...

In mathematics we say

sqrt(-1) = i This is a definition

Now i^2 = -1 (e.g. sqrt(4) = 2 ; therefore 2^2 = 4 )

i^2 = sqrt(-1)*sqrt(-1)

This can be written as

i^2 = sqrt((-1)*(-1)) (e.g. sqrt(2)*sqrt(2) = sqrt(2*2) )

so i^2 = sqrt(1) (as (-1)*(-1) = 1 )

i^2 = 1 (as sqrt(1) = 1 )

taking the square root of both sides

i = 1

But at the beginning i = sqrt(-1)

So sqrt(-1) = 1

this is wrong bro

 

[Tom Riddle]

(-1) ^ 1/2 * (-1 )^ 1/2 = -1(1/2+1/2)= -1
hence
i^2 = -1
i = sqrt(-1)
back to the def

mula indan waradda gawata awilla waradda nokara aimath mulata yanawa.

 

[kasuncs]

Definition is
i^2=-1

It is not sqrt(-1)=i

Square root function only defined for positive numbers.




Edit: Error corrected.

 

[Tom Riddle]

Definition is
i^2=-1

It is not sqrt(-1)=i

Both are correct

 

[Tom Riddle]

Definition is
i^2=-1

It is not sqrt(-1)=i

Square root function only defined for positive numbers.

put (-1)^(1/2)= -i or i

Oh no this is so wrong macho...

 

[koondeGoda]

mula indan waradda gawata awilla waradda nokara aimath mulata yanawa.

What ? Not clear


No worries Mr.SmartAss riddle in action

 

[kasuncs]

Both are correct

A complex number is a number comprising a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1.[1] The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.

http://en.wikipedia.org/wiki/Complex_numbers

 

[Tom Riddle]

A complex number is a number comprising a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1.[1] The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.

http://en.wikipedia.org/wiki/Complex_numbers

Can you please read the whole article?

"This difficulty eventually led to the convention of using the special symbol i in place of sqrt(-1) to guard against this mistake" - check it out.

And check out other sites, maths books etc. It's all over the place.

We don't need another definition for -1. We need a definition for sqrt(-1). That incidentally leads to i^2 = -1

 

[December]

Hmmm Hmmmm

The rule is for

sqrt(a)*sqrt(b) to be equal to sqrt(a*b) at least one of a and b should be positive...

This solve the mistake...

although sqrt(2)*sqrt(2) = sqrt(2*2)
sqrt(-1)*sqrt(-1) != sqrt ((-1)*(-1))

 

[Chathurangaabey]

i^2 = sqrt((-1)*(-1)) (e.g. sqrt(2)*sqrt(2) = sqrt(2*2) )

this is wrong... think this with +,- values...

i.e. sqrt(4) = 2 is wrong it should be +or- 2