The square root of negative 1 is “i”. The “i” referrs to an imaginary number. When you square a number (e.g. 2^2 ) the result will always be positive. This is because you are multiplying the number with itself, and a negative number multiplied by another negative number will be positive. So -2 * -2 = 4, -3 * -3 = 9, and so on.
A square root is the inverse of this. It attempts to find what the original number was that was squared, so sqrt(4) = 2, sqrt(9) = 3, and so on. However, what do you do if you have sqrt(-4)? There’s no way for a square to result in a negative number, so the result must be imaginary. So sqrt(-4) = 2i, sqrt(-9) = 3i, and so on. As such, sqrt(-1) = i.
For the next part, when you divide one number by another, it is sometimes referred to as [first number] over [second number].
Finally, 8, well, sounds like “ate”.
So sqrt(-1)/8 = i/8 = i over eight= I over ate.
(Sorry if this came off as condescending near the end, I’m trying to be thorough in case you aren’t a native English speaker)
The square root of negative 1 is “i”. The “i” referrs to an imaginary number. When you square a number (e.g. 2^2 ) the result will always be positive. This is because you are multiplying the number with itself, and a negative number multiplied by another negative number will be positive. So -2 * -2 = 4, -3 * -3 = 9, and so on.
A square root is the inverse of this. It attempts to find what the original number was that was squared, so sqrt(4) = 2, sqrt(9) = 3, and so on. However, what do you do if you have sqrt(-4)? There’s no way for a square to result in a negative number, so the result must be imaginary. So sqrt(-4) = 2i, sqrt(-9) = 3i, and so on. As such, sqrt(-1) = i.
For the next part, when you divide one number by another, it is sometimes referred to as [first number] over [second number].
Finally, 8, well, sounds like “ate”.
So sqrt(-1)/8 = i/8 = i over eight= I over ate.
(Sorry if this came off as condescending near the end, I’m trying to be thorough in case you aren’t a native English speaker)
It seems I was only having trouble with the connecting “eight” to “ate”, but damn, this is a solid explanation of the other parts too!
Thank you! I only got as far as i divided by 8… But now I kinda get it (-: |>
Very thorough. I’ll just add stylization: √−̅1̅ = 𝑖
Edit: minus
Forgot the minus