DeMoivre's Theorem and Euler FormulaVideos, worksheets, games and acivities to help PreCalculus students learn how to use DeMoivre's Theorem to raise a complex number to a power and how to use the Euler Formula can be used to convert a complex number from exponential form to rectangular form and back
DeMoivre's Theorem : We know how to multiply complex numbers, but raising complex numbers to a high integer power would involve a lot of computation. Fortunately we have DeMoivre's Theorem, which gives us a more simple solution to raising complex numbers to a power.DeMoivre's Theorem can also be used to calculate the roots of complex numbers. DeMoivre's Theorem uses the trigonometric form of complex numbers.
Using DeMoivre's Theorem to Raise a Complex Number to a Power
Euler Formula : One formula that is used frequently to rewrite a complex number is the Euler Formula. The Euler Formula can be used to convert a complex number from exponential form to rectangular form and back. The Euler Formula is closely tied to DeMoivre's Theorem, and can be used in many proofs and derivations such as the double angle identity in trigonometry.
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