:^)

and ?

>>7989011
If anyone here can't immediately see why this is wrong then he should kill himself

[eqn] \sqrt{\frac{-1}{1}}[/eqn]
isn't the same as
[eqn] {\frac{\sqrt{-1}}{\sqrt{1}}}[/eqn]

>>7989064
Not OP, but can you explain why?

File: 1456021745805.png (387KB, 450x472px) Image search: [Google]

387KB, 450x472px

>implying the square root function is still continuous on all of C and the third step is valid
>mfw

>>7989064
They both equal i though.
:^)

>>7989011
thing is: i is NOT defined as the square root of -1 but rather has the propertie to have its square being -1. because if you use i = sqrt(-1) you get problems as in OPs picture

>>7989112
sqrt(9/3) is not the same is sqrt(9) /sqrt (3)
DUMBASS

>>7989194
But we're not talking about 9 and 3
We're talking about 1 and -1

>>7989194
yes it is

>>7989137
Actually, that's not the problem
>>7989087
Here :
[eqn]\dfrac{\sqrt{1}}{\sqrt{-1}}=\dfrac{1}{\sqrt{-1}}=\dfrac{1}{i}=-i[/eqn]
whereas
[eqn]\sqrt{\dfrac{1}{-1}}=\sqrt{-1}=i[\eqn]
As >>7989089 said, is has to do with the fact that [math]\sqrt{x}[\math] isn't continuous on C

File: iFunny - 4_7_2016 4_47_54 PM.jpg (65KB, 460x460px) Image search: [Google]

65KB, 460x460px

>>7989194
>sqrt(3) =/= 3/sqrt(3)
Wat

>>7989207
Failed :
[eqn] \dfrac{\sqrt{1}}{\sqrt{-1}}=\dfrac{1}{\sqrt{-1}}=\dfrac{1}{i}=-i[/eqn]
and
[eqn] \sqrt{\dfrac{1}{-1}}=\sqrt{-1}=i[/eqn]

>>7989207
>Actually, that's not the problem
yes it is. or rather: that is where he got the idea from.
sqrt(-1) is simply not defined. there his whole problem is not arising anywhere.

>sqaureroot of -1

The same number times itself cannot be a negative number dipshit.

>>7989216
second part is supposed to be :
[eqn] \sqrt{\dfrac{1}{-1}}=\sqrt{-1}=i [/eqn]

>>7989011
The square root of -1 isn't equal to the square root of -1 divided by -1.

>>7989220
>hasn't gotten to complex numbers
I remember middle school

>>7989011
squareroot of -1 is not defined.

>>7989233
he is right though i squared is defined however i does not equal sqrt of -1, i see u havent left highschool yet.

>>7989011
Math major here graduating this semester. What is wrong with this?

>>7989245
That's true. But he said "a number times itself can not be negative" a direct contradiction to the exact definition of the number i

>>7989246
What's wrong is that sqrt(1)/sqrt(-1) is -i

>>7989011
The second equality isn't true. That's why you're tripping. in C, i =/= 1/i

>>7989246
Complex numbers have their own set of algebraic rules. You can not apply real number algebra to complex numbers. When I was in uni, there was a whole course on complex number fields and their applications.