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The image shows a set of mathematical exercises where the task is to find roots using De Moivre's Theorem. Here's a breakdown of the visible problems that require solving:

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### 1. **Hallar las raíces indicadas en cada caso usando el teorema de Moivre:**
   Find the indicated roots in each case using De Moivre's Theorem.

- **a.** Las **raíces cúbicas** de \( 1 \)
  
- **b.** Las **raíces quintas** de \( 1 \)

- **c.** Las **raíces cuartas** de \( 1 - \sqrt{3}i \)

- **d.** Las **dos raíces cuadradas** de \( 1 + i \)

- **e.** Las **raíces sextas** de \( 64[\cos 78^\circ + i \sin 78^\circ] \)

- **f.** Los **ocho raíces** de \( 2 + 5i \)

- **g.** Las **cinco de** \( -3 + i \)

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These are complex numbers, and to solve them, De Moivre's Theorem will be used. The theorem expresses a complex number in polar form, allowing the extraction of roots.

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Here are some related questions:
1. Do you need a quick reminder on how to apply De Moivre's Theorem?
2. Would you like help converting complex numbers to polar form?
3. Do you want an example of extracting roots using De Moivre's theorem?
4. Would you prefer step-by-step instructions for each type of root?
5. Are there any particular parts of this set of problems you'd like to clarify?

**Tip:** Always express complex numbers in polar form before applying De Moivre’s theorem—it simplifies root extraction significantly!

Hallar las raíces indicadas en cada caso usando el teorema de Moivre: a) Las raíces cúbicas de 1, b) Las raíces quintas de 1, c) Las raíces cuartas de 1 - √3i, d) Las dos raíces cuadradas de 1 + i, e) Las raíces sextas de 64[cos 78° + i sen 78°], f) Los ocho raíces de 2 + 5i, g) Las cinco de -3 + i.

Find the cubic, fifth, fourth, and other roots of complex numbers using De Moivre's Theorem. This problem set involves converting complex numbers into polar form and extracting their roots, covering concepts like the sixth roots of 64[cos 78° + i sin 78°] and the fourth roots of 1 - √3i.

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