Quick De Moivre's Theorem question

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In summary, Quick De Moivre's Theorem is a mathematical formula that allows for quick calculation of complex powers of a complex number. To use it, the complex number must be converted into polar form. The main difference between Quick De Moivre's Theorem and De Moivre's Theorem is that the former only applies to complex numbers. It is useful in simplifying calculations, especially in fields such as engineering and statistics. However, it has limitations and can only be used for finding complex powers and assumes the number is in polar form.
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Homework Statement


In example 1 on this webpage;
http://www.cliffsnotes.com/study_guide/De-Moivres-Theorem.topicArticleId-11658,articleId-11634.html [Broken]
(√3 + i)^7

You'll see that the angle is inserted in degrees, and then in the working out the degree angles are multiplied by the power of 7, to give 210°

If the angle had been inserted in radians i.e. ∏/6 and multiplied by the power of 7 also, to give 7∏/6 in the working out (instead of 210°), would this be equally valid?
 
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π radian corresponds to 180°. 210° is equivalent to (210/180) π = 7π/6.

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1. What is Quick De Moivre's Theorem?

Quick De Moivre's Theorem is a mathematical formula that allows for the quick calculation of complex powers of a complex number. It is an extension of De Moivre's Theorem, which only applies to real numbers.

2. How do you use Quick De Moivre's Theorem?

To use Quick De Moivre's Theorem, you first need to convert the complex number into polar form. Then, you can use the formula (r^n * cos(nθ) + i * r^n * sin(nθ)) to find the complex power of the number.

3. What is the difference between Quick De Moivre's Theorem and De Moivre's Theorem?

The main difference between the two theorems is that Quick De Moivre's Theorem applies to complex numbers, while De Moivre's Theorem only applies to real numbers. Quick De Moivre's Theorem also allows for a faster calculation of complex powers.

4. Why is Quick De Moivre's Theorem useful?

Quick De Moivre's Theorem is useful because it simplifies the calculation of complex powers, which can be tedious and time-consuming using other methods. This theorem is particularly helpful in fields such as engineering, physics, and statistics.

5. Are there any limitations to using Quick De Moivre's Theorem?

Yes, there are a few limitations to using Quick De Moivre's Theorem. It only applies to finding complex powers and cannot be used for other operations such as addition or multiplication. Additionally, it assumes that the complex number is in polar form, so it may not work for numbers in other forms.

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