Complex Numbers rev 1

Transcript

1. Complex Numbers Introduction
2. Peixian Wang, AI developer plains.guru peixian@plains.guru @thopterfoundry
3. Math has a dirty secret…
4. Everything in mathematics is a choice!
5. Doesn’t seem like much choice with…
6. So where is the choice?
7. 6 4 =? 9/2 =? p (2) =? p ( 36) =?
8. Complex Numbers? >What does it mean? >What’s the point?
9. Complex Numbers? How do we work with
10. i
11. You might know:
13. Let’s start simple:
14. Taking the Inverse
15. Vectors?
16. Vectors?
17. Vectors?
18. What about multiplication?
19. What if we multiplied it by a negative number?
20. Is there a pattern?
21. What if we drew a line between the points?
22. We found it!
23. What if we form the pattern through rotation?
27. What does this even mean?
28. What does this even mean?
29. If green areas are formed by multiplication…
30. If green areas are formed by multiplication… And it takes 2 greens to get from 1 to -1…
31. If green areas are formed by multiplication… And it takes 2 greens to get from 1 to -1… In other words…
32. If green areas are formed by multiplication… And it takes 2 greens to get from 1 to -1… In other words… 1 ⇤ x 2 = 1
33. Then… If 1 ⇤ x 2 = 1 x = i
34. Then… If 1 ⇤ x 2 = 1 x = i We found it!