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11. Graphing Complex Numbers

Powers of Complex Numbers (DeMoivre's Theorem)

11. Graphing Complex Numbers

Powers of Complex Numbers (DeMoivre's Theorem)

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Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem) Example 1

Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem) Example 1

Complex Roots Example 1

Complex Roots Example 1

Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)

Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)

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De Moivre's Theorem powers of Polar Complex Numbers

De Moivre's Theorem powers of Polar Complex Numbers

Complex Numbers Polar Form Product De Moivre's Theorem and nth Root

Complex Numbers Polar Form Product De Moivre's Theorem and nth Root

Raise a Complex Number in Polar Form to a Power - Demoivre's Theorem

Raise a Complex Number in Polar Form to a Power - Demoivre's Theorem

Examples of nth Roots of Complex Numbers

Examples of nth Roots of Complex Numbers

Finding the nth roots of a complex number in polar form

Finding the nth roots of a complex number in polar form

Complex Numbers Polar Form Product De Moivre's Theorem and nth Root

Complex Numbers Polar Form Product De Moivre's Theorem and nth Root

Determining the Nth Roots of a Complex Number

Determining the Nth Roots of a Complex Number

Finding nth Roots of a Complex Number

Finding nth Roots of a Complex Number

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Multiple Choice

Given $z = 3 C i S (\frac{4 π}{5})$ , calculate $z^{5}$ .

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [4(cos 15° + i sin 15°)]³

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 10° + i sin 10°)]³

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 80° + i sin 80°)]³

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 40° + i sin 40°)]³

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [1/2 (cos π/12 + i sin π/12)]⁶

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [1/2 (cos π/10 + i sin π/10)]⁵

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ [√2 (cos 5π/6 + i sin 5π/6)]⁴

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ [√3 (cos 5π/18 + i sin 5π/18)]⁶

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (1 + i)⁵

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (1 − i)⁵

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ (√3 − i)⁶

Textbook Question

In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ (√2 − i)⁴

Textbook Question

In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex square roots of 9(cos 30° + i sin 30°)

Textbook Question

In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex square roots of 25(cos 210° + i sin 210°)

Textbook Question

In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 8(cos 210° + i sin 210°)

Textbook Question

In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 27(cos 306° + i sin 306°)

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fourth roots of 81 (cos 4π/3 + i sin 4π/3)

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of 32 (cos 5π/3 + i sin 5π/3)

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fifth roots of 32

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 64

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 1

Textbook Question

In Exercises 69–76, find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex sixth roots of 1 + i

Textbook Question

In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 20° + i sin 20°)]³

Textbook Question

In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [4(cos 50° + i sin 50°)]³

Textbook Question

In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [12 (cos π/14 + i sin π/14)]⁷

Textbook Question

In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. _ (1−i√3)²

Textbook Question

In Exercises 25–29, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (−2 − 2i)⁵

Textbook Question

In Exercises 30–31, find all the complex roots. Write roots in polar form with θ in degrees. The complex cube roots of 125(cos 165° + i sin 165°)

Textbook Question

In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex fourth roots of 16 (cos 2π/3 + i sin 2π/3)

Textbook Question

In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex cube roots of 8i

Textbook Question

In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex cube roots of −1

Textbook Question

In Exercises 32–35, find all the complex roots. Write roots in rectangular form. The complex fifth roots of −1 − i

Textbook Question

In Exercises 5–7, perform the indicated operation. Leave answers in polar form. [2(cos 10° + i sin 10°)]⁵

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