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Find The Indicated Power Using De Moivre's Theorem


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Find The Indicated Power Using De Moivre's Theorem. (a+bi) n = (r cisθ) n = r n cis (nθ) r cisθ means r (cosθ + isinθ) where r = √ (a 2 + b 2) and θ = arctan (b/a). Demoivre’s theorem is very useful in calculating powers of complex numbers, even fractional powers.

How to Use De Moivre’s Theorem to Find Powers of Complex Numbers
How to Use De Moivre’s Theorem to Find Powers of Complex Numbers from mathsathome.com

We illustrate with an example. We are using the de moivre's theorem, to find the indicated power of a complex number. Demoivre’s theorem is very useful in calculating powers of complex numbers, even fractional powers.

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How to Use De Moivre’s Theorem to Find Powers of Complex Numbers

Demoivre’s theorem is very useful in calculating powers of complex numbers, even fractional powers. This involves writing the complex number in**. And integer n, (cos ? + i sin ?)^n = cos (n?) + i sin (n?).

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