IMPOSSIBLE i²=1 #maths

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√-1/√1=i
√1/√-1=-i
they're not equal

apple

Due to the way i is defined √(-a/b) ≠ √(a/-b), so whenever something like (a/-b) occurs the general rule is to multiply both the numerator and the denominator by -1 to get (-a/b) so that we can then take this under the root and have √(-a/b) = i√(a/b), if √(-a/b) = √(a/-b) were true things like i = - i and i^2 = ±1 would happen it could also lead to something like √x = -1 having actual roots which is obviously not possible (even in the complex plane).

frendlyleaf

very few caught that mistake here is the assumption that don't work here which is:- √(a÷b) ≠√(a)÷√(b).
and also √(axb)≠√ax√b is not always equal. even my maths teacher was surprised when I showed her this 'magic' 😅

abhshk

Remember that n-th root of complex number in an n element array, so sqrt(-1) is acctually an array {-i, i} and cannot be used in algebraic ewuation

phoenig

In general, if k is an integer
i^(4k) = 1
i^(4k+1) = √-1 = i
i^(4k+2) = -1
i^(4k+3) = -i

Then √-1/√1 = √-1 = i
And √1/√-1 = 1/i = i^(-1) = i^(-4+3) = -i

Hence √(-1/1) ≠ √(1/-1)

πΣυφ-μξ

i²=-1. i²≠1
i⁴ⁿ=1
I study in complex number

sarthikthakur

Sqrt is ONLY defined for real numbers >= 0, and NOT defined for everything else. So usual rules dont apply.
Saying i = sqrt(-1) is wrong, i is defined so that i² = -1.

ant

√(a/b)=√a/√b if a, b≥0, √-1/√1≠√1/√-1

lakshyasaxena

1/-1 should be in its standard forrm as it is a rational no

AtharvPowar-umcx

Is it the mistake :- √(a/b)=√a/√b when a, b > 0, but you put√( 1/-1)= √1/√-1

GoutamPattajoshi

negative number in root does not shrink

sunnyghosh

The issue with the proof is that sqrt(a/b) only the same as sqrt(a)/sqrt(b) if a and b positive.

kevinsolari

(a*b)^c is only true if a, b is real number.
√-1 is not

BobChess

√1≠1 but is actually ±1 and in this case, it is -1

gaminglegends

Under root two negetive numbers are not multiple, because this property not holding

wildanimals

You are violating simple rules of exponential and square roots
√(1/-1) not equal to √1/√-1
Since when you seperate square root between two terms, term inside square root should be positive

AAlok_Yadav_AA

The biggest mistake is i^2 = -1 not 1
bruh, you guys didn't notice?

UMARX

Its wrong. You can't just swipe the signs between the denominator and numerator when they fall under square roots. Besides √1 will become 1 and √-1 will remain the same.

AnishMukherjee-kx

Brother I love this background sond can you plz tell this song name plz

ApesProgt

I might be wrong but I knew that u can't form equations without a variable. Plz correct me if I'm wrong

souvik

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