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De Moivre's Theorem: Legacy of a Brilliant French Mathematician

Learn about De Moivre, the French mathematician persecuted for his beliefs, who moved to England and revolutionized trigonometry with his theorem in the field of complex numbers. Discover the power of De Moivre's theorem and its applications through analysis and probability. Make conjectures, find identities, and explore the binomial expansion using this fantastic theorem.

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De Moivre's Theorem: Legacy of a Brilliant French Mathematician

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  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:

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