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This feels wrong. I love it. (sopuli.xyz)

submitted 2 days ago by hydroptic@sopuli.xyz to c/science_memes@mander.xyz

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[-] owenfromcanada@lemmy.world 11 points 2 days 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.

[-] rtxn@lemmy.world 7 points 2 days ago* (last edited 2 days 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 that can be expanded to a * (1, 0) + b * (0, 1)). AB's length is (1, 0), AC's length is (0, 1), and BC's length will also be a complex number.

I think.

[-] TowardsTheFuture@lemmy.zip 1 points 2 days 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.