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owenfromcanada@lemmy.world ⁨1⁩ ⁨month⁩ ago

If AB = i and BC = 0, then B would be in the same 2D space as C, but one of them would be “above” the other in 3D space (which doesn’t exist in this context, just as sqrt(-1) doesn’t exist in the traditional sense).

So this triangle represents a 2D object that is “standing up” on the page.

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rtxn@lemmy.world ⁨1⁩ ⁨month⁩ ago
It makes sense if you represent complex numbers as (a, b) pairs, where a is the real part and b is the imaginary part (just like the popular a + bi representation). AB’s length is (1, 0), AC’s length is (0, 1), and BC’s length will also be a complex number.

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- TowardsTheFuture@lemmy.zip ⁨1⁩ ⁨month⁩ ago
  Yes. Also if you think of i as a 90° rotation (with a length of the scalar coefficient infront of i, in this case 1) . Thus one rotates you outwards away from the 2D plane, and two of those gets you back to the 2D plane, just going the other direction.
  
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