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I love the visualization on acko.net but for whatever reason, unlike apparently many of you, I still don't understand the topics he's trying to explain. As jus

I love the visualization on acko.net but for whatever reason, unlike apparently many of you, I still don't understand the topics he's trying to explain. As just one example on step 18 of the first major visualization it says "And that's actually a remarkable thing, because it means our invented rule has created a square root of −1. It's the number 1∠90∘" WAT?! I'm sure someone skilled at math understands that but as a lamer at math I have no idea how that explains that the rule invented the square root of -1. Nothing before that has mentioned square roots or how this vector + rotation has any relation to them.

milu 12y ago
I had the same reaction. There should be a few words showing that we now have a point which multiplied by itself (rotated by 90° around 0) goes to -1. So this number is the square root of -1.
- qiemem 12y ago
  The next slide shows that.
qiemem 12y ago
I think that particular slide was poorly worded. He's actually introduction a consequence of the rules, but not saying it's an obvious consequence. Slide 19 shows how (1∠90∘)2 = -1.
vitd 12y ago
I don't want to disparage the author's hard work, as it was quite beautiful to look at, but as someone who already understands what he's talking about, I felt this was a terrible way to present it. (Like I say, it looked great, but I don't think it would aid a new student learning about complex numbers at all.) The notation he invents is confusing, too. That "1∠90°" just means a vector with length 1 and pointing 90° from the X-axis (which the author later changes to the Y-axis for no apparent reason). In my opinion, polar coordinates (which is what the notation represents) are a fascinating tool that can be very helpful. I use them quite a bit. Conflating that with complex numbers is confusing if you don't already understand both polar coordinates and complex numbers, in my opinion.
- sigterm 12y ago
  Hmm I don't think he invented the polar notion. It is a standard representation of complex number to me and I have certainly used it back in school (I studied EE). This notion actually simplifies multiplication significantly.

milu 12y ago

I had the same reaction. There should be a few words showing that we now have a point which multiplied by itself (rotated by 90° around 0) goes to -1. So this number is the square root of -1.

qiemem 12y ago
The next slide shows that.

qiemem 12y ago

I think that particular slide was poorly worded. He's actually introduction a consequence of the rules, but not saying it's an obvious consequence. Slide 19 shows how (1∠90∘)2 = -1.

vitd 12y ago

I don't want to disparage the author's hard work, as it was quite beautiful to look at, but as someone who already understands what he's talking about, I felt this was a terrible way to present it. (Like I say, it looked great, but I don't think it would aid a new student learning about complex numbers at all.) The notation he invents is confusing, too. That "1∠90°" just means a vector with length 1 and pointing 90° from the X-axis (which the author later changes to the Y-axis for no apparent reason). In my opinion, polar coordinates (which is what the notation represents) are a fascinating tool that can be very helpful. I use them quite a bit. Conflating that with complex numbers is confusing if you don't already understand both polar coordinates and complex numbers, in my opinion.

sigterm 12y ago
Hmm I don't think he invented the polar notion. It is a standard representation of complex number to me and I have certainly used it back in school (I studied EE). This notion actually simplifies multiplication significantly.