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Imaginary Numbers Are Real – YouTube Series

4 points by pedrodelfino 9y ago

pedrodelfino 9y ago
The greatest audiovisual content on the topic I have ever seen: Part 1 - https://www.youtube.com/watch?v=T647CGsuOVU https://www.youtube.com/watch?v=T647CGsuOVU Part 2 - https://www.youtube.com/watch?v=2HrSG0fdxLY https://www.youtube.com/watch?v=2HrSG0fdxLY Part 3 - https://www.youtube.com/watch?v=N9QOLrfcKNc https://www.youtube.com/watch?v=N9QOLrfcKNc Part 4 - https://www.youtube.com/watch?v=DThAoT3q2V4 https://www.youtube.com/watch?v=DThAoT3q2V4 Part 5 - https://www.youtube.com/watch?v=65wYmy8Pf-Y https://www.youtube.com/watch?v=65wYmy8Pf-Y Part 6 - https://www.youtube.com/watch?v=z5IG_6_zPDo https://www.youtube.com/watch?v=z5IG_6_zPDo Part 7 - https://www.youtube.com/watch?v=YHvR8siIiD0 https://www.youtube.com/watch?v=YHvR8siIiD0 Part 8 - https://www.youtube.com/watch?v=iecUL8_OxrU https://www.youtube.com/watch?v=iecUL8_OxrU Part 9 - https://www.youtube.com/watch?v=dLn5H69lS0w https://www.youtube.com/watch?v=dLn5H69lS0w Part 10 - https://www.youtube.com/watch?v=pNp8Qf20-sA https://www.youtube.com/watch?v=pNp8Qf20-sA Part 11 - https://www.youtube.com/watch?v=0hiWbdc8QEk https://www.youtube.com/watch?v=0hiWbdc8QEk Part 12 - https://www.youtube.com/watch?v=DpUmrKOQhAM https://www.youtube.com/watch?v=DpUmrKOQhAM Part 13 - https://www.youtube.com/watch?v=4MmSZrAlqKc https://www.youtube.com/watch?v=4MmSZrAlqKc
Koshkin 9y ago
Nice videos! Reminds me of the excellent Visual Complex Analysis by Needham. Just a general warning: one problem with trying to use visualization to help better understand and solve problems involving complex numbers is that this only works in one dimension. While it is easy for us to imagine real spaces up to three dimensions, trying to get an intuition about even a two-dimensional complex space by trying to "visualize" it seems to be so difficult as to be not worth the effort, and all we are left with is formal computational rules. (Incidentally, these rules are not so bad, and thus being able to "see" them at work in one-dimensional case, while helpful in getting comfortable with the idea, quickly loses its importance even in one dimension.)

4 points by pedrodelfino 9y ago

The greatest audiovisual content on the topic I have ever seen: Part 1 - https://www.youtube.com/watch?v=T647CGsuOVU https://www.youtube.com/watch?v=T647CGsuOVU Part 2 - https://www.youtube.com/watch?v=2HrSG0fdxLY https://www.youtube.com/watch?v=2HrSG0fdxLY Part 3 - https://www.youtube.com/watch?v=N9QOLrfcKNc https://www.youtube.com/watch?v=N9QOLrfcKNc Part 4 - https://www.youtube.com/watch?v=DThAoT3q2V4 https://www.youtube.com/watch?v=DThAoT3q2V4 Part 5 - https://www.youtube.com/watch?v=65wYmy8Pf-Y https://www.youtube.com/watch?v=65wYmy8Pf-Y Part 6 - https://www.youtube.com/watch?v=z5IG_6_zPDo https://www.youtube.com/watch?v=z5IG_6_zPDo Part 7 - https://www.youtube.com/watch?v=YHvR8siIiD0 https://www.youtube.com/watch?v=YHvR8siIiD0 Part 8 - https://www.youtube.com/watch?v=iecUL8_OxrU https://www.youtube.com/watch?v=iecUL8_OxrU Part 9 - https://www.youtube.com/watch?v=dLn5H69lS0w https://www.youtube.com/watch?v=dLn5H69lS0w Part 10 - https://www.youtube.com/watch?v=pNp8Qf20-sA https://www.youtube.com/watch?v=pNp8Qf20-sA Part 11 - https://www.youtube.com/watch?v=0hiWbdc8QEk https://www.youtube.com/watch?v=0hiWbdc8QEk Part 12 - https://www.youtube.com/watch?v=DpUmrKOQhAM https://www.youtube.com/watch?v=DpUmrKOQhAM Part 13 - https://www.youtube.com/watch?v=4MmSZrAlqKc https://www.youtube.com/watch?v=4MmSZrAlqKc

Koshkin 9y ago

Nice videos! Reminds me of the excellent Visual Complex Analysis by Needham. Just a general warning: one problem with trying to use visualization to help better understand and solve problems involving complex numbers is that this only works in one dimension. While it is easy for us to imagine real spaces up to three dimensions, trying to get an intuition about even a two-dimensional complex space by trying to "visualize" it seems to be so difficult as to be not worth the effort, and all we are left with is formal computational rules. (Incidentally, these rules are not so bad, and thus being able to "see" them at work in one-dimensional case, while helpful in getting comfortable with the idea, quickly loses its importance even in one dimension.)