4 ms·

I'm curious. I seem to be missing something, because I feel like what you're saying tracks very much with the "alternative interpretation". That is, I don't see

• vishnugupta 5y ago
  For me it is about expressing a concept as compactly as possible. In case of Nautilus they first ask us to imagine -1 as 180° and then proceed say half of it as 90° rotation and finally give it a name i. For some this may work fine as a way to understand. However it gets awkward to further explain. If 𝑖 stands for half of -1 (as they say) then does that mean 𝑖 == -(1/2)? If not then why not? and so on. Compare that with: 𝑖 is a unit of rotation which is 90°. That's it. Using this as a base it's easier to explain why 𝑖² = -1 (two units of anti-clockwise rotation) or why 𝑖³ = -i (three units of anti-clockwise rotation is same as one unit of clockwise rotation) and so on. More fundamentally, they ask us to imagine an operation on 1-d (-1) as happening through 2-d (180° rotation). It seems convoluted way to introduce 𝑖. I'd rather explain 𝑖 from the first principles and proceed to show its consequences such as 𝑖² = -1.
  • garmain 5y ago
    Thank you for your response. I see where you are coming from. I think because I don't interpret their text as saying that i is "half of -1" but "half of the rotation that would lead to -1" I consider your description equivalent. In fact I am struggling to interpret their text to say "half of -1". Regardless, I see your point.