[dsrtsage]

The new math

1 = 1
1 = 1 * 1
1 = 1²
1=√(1²)
1 = √1 * √1

1 = (-1) * (-1)
1 = (-1)²
1 = √(-1)²
1 = √(-1) * √(-1)
1 = i * i
1 = i²
1 = -1

[dayglored]

I think the error is in this step:

1 = (-1)²
1 = √(-1)²

While it is true that the square of 1 and the square of -1 are the same, that does not mean that 1 = -1

But your post is a neat challenge, and made me stop and think... thanks!

[kvanbrunt2]

curious why you posted this as most things multiplied by themselves = 1 as i recall the identity principle. but 1 doesn’t = -1

[jpsb]

your "1 = i * i" is incorrect by definition.

From Wiki
"An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = -1. "