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De Moivres Theorem Powers of Complex Numbers

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De Moivres Theorem We use this theorem to: I.Simplify complex numbers raised to a power. II.Solve certain types of equations, or find the nth roots of a complex number. I.POWERS

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De Moivres Theorem: You need to know: A. Convert rectangular form into trigonometric form B. Simplify fractions C. Simplify radicals

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Problem 1 Then, find the angle:

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Your turn…

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Practice: Use De Moivres theorem to find (-1 + i3 ) 12 a. Convert the complex number to trig form: b. Then use De Moivres Theoem to find the value Answer: 4096

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De Moivres Theorem Powers of Complex Numbers Grab your book and calculator

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Who was De Moivre A brilliant French mathematician who was persecuted in France because of his religious beliefs. De Moivre moved to England where he tutored mathematics privately and became friends with Sir Isaac 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 Moivres theorem.

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Warm - up 1. (3 - 2i) 5 2. (5 - 4i) 3 = i = i

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