1 / 6

Complex numbers 4

Complex numbers 4. De Moivre’s Theorem. www.ibmaths.com. Who was De Moivre?. A brilliant French mathematician who was persecuted in France because of his religious believes. De Moivre moved to England where he tutored mathematics privately and became friends with Sir Issac Newton.

kiri
Télécharger la présentation

Complex numbers 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Complex numbers 4 De Moivre’s Theorem www.ibmaths.com

  2. Who was De Moivre? A brilliant French mathematician who was persecuted in France because of his religious believes. De Moivre moved to England where he tutored mathematics privately and became friends with Sir Issac Newton. De Moivre made a breakthrough in the fields of probability (writing the Doctrine of Chance), but more importantly for IB HL students he moved trigonometry into the field of analysis through complex numbers with De Moivre’s theorem.

  3. Powers of z. Make a conjecture for

  4. But can we prove it? Assume n=1 the statement is true. Let n = k, so that: Now find

  5. So what is the use? Find an identity for using Mr. De Moivre’s fantastic theorey Remember the binomial expansion: Apply it: Cancel out the imaginery numbers:

  6. Now try these:

More Related