Algebra - Ch. 24: Complex Numbers (16 of 28) How to Prove: -1=1

We will learn how to prove 1=-1???

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[integrantedavidanoturna]

But why is that a forbidden step? I can see it should be forbidden, but what does it mean? Sqrt(ab)=sqrt(a)*sqrt(b) for positive numbers, and this property is even used when taking sqrt(-4), i.e. So why is it not true that

[urosjankovic]

The error occurred because the n-th root of a complex number z is defined as:
z^(1/n) = n√r(cos((φ+2kπ)/2) + i*sin((φ+2kπ)/2))
Where r = |z|, φ = arg(z) and k ∈ ℤ. Here, n√r is n-th root of a real number (different from root of a complex number) and it's result is a single number. The result of n-th root of a complex number on the other hand is not a single number, but a set of numbers from ℂ. Thus, one cannot say
i = √-1,
since square root (or any even root) of a real number isn't defined for negative real numbers, and square root of a complex number returns a set of numbers and not a single number. The correct way of writing this expression would be:
i ∈ √-1 = {i, -i}.

[mdhasnain_]

To all who think sqrt(x²)=±x
Dear all, let me correct you, sqrt (x²)= mod(x) and it's how it is defined. So no one can argue with the definition. Now put x=1 so, sqrt(1²)=mod(1)=1.
Btw I could not figure out mistake in the video

[RnBoy]

Before seeing the answer, my observation is that sqrt(1) is not just =1, but ±1, because -1^2 is also = sqrt(1)

[aame]

But the square root of one could be two answers +1 and -1...

[joeanil]

I do understand that you were trying prove that -1=1, but Why? Is there any application or theory where it is applicable.

[renatachavessoares]

is just do

-1²=1
1²=1
√1=-1
√1=1
-1=1

[cars_lovers]

no 1½=+1 or -1
so u take the logical value
-1=-1

[omegamath]

Your explanation is wrong from 0:40, not from 0:50.
Square root (-1) times (-1) is -1 by the definition of square root
I think Euler's Identity has some problems, but not mine.

[nf]

I can smell the Pen ink...it smell good

[rutweakchacha]

Prove 1 = -1 without the help of complex numbers

[shmayisrael]

I subscribed! :D
I love your Electrical Engineering Vids! Keep up the good work.

[TempUserTempAC]

It's too simple
-1² = 1
-1 = √1
-1 = 1😂

[nasa]

So did you just prove to us that “1=-1” or “1≠-1”, due to that violation at the end? You kinda left me hanging...🤨🧐☹️

[colloidalsilver]

so confused... why would you even have to sqrt on the left side to begin with?

[tuskiomisham]

Well, the sqrt(1) is ±1, not 1... -1 = sqrt(1) = 1.

All the math checks out, you just forgot something at the end.