MHB Find the square roots of 4*sqrt(3)+4(i)

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The discussion revolves around finding the square roots of the expression 4*sqrt(3) + 4(i). The original poster expresses confusion over the question, indicating a lack of familiarity with the material, possibly due to differences in teaching styles. A participant suggests using Euler's formula and de Moivre's theorem to solve the problem, but the original poster admits to not understanding these concepts. The conversation highlights a gap in knowledge regarding complex numbers and their properties. Understanding these mathematical principles is essential for solving the given problem effectively.
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So I have a study guide for my final which was written by a different professor from my actual professor. So I don't understand the question, I don't know if it's because my professor did not teach this or if the wording is different from what I'm used to:

Find the square roots of 4*sqrt(3)+4(i)
 
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Elissa89 said:
So I have a study guide for my final which was written by a different professor from my actual professor. So I don't understand the question, I don't know if it's because my professor did not teach this or if the wording is different from what I'm used to:

Find the square roots of 4*sqrt(3)+4(i)

I would let:

$$y=8\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)=8e^{\Large\frac{\pi}{6}i}$$

Can you proceed?
 
MarkFL said:
I would let:

$$y=8\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)=8e^{\Large\frac{\pi}{6}i}$$

Can you proceed?

No, i don't know what the right side means.

- - - Updated - - -

Elissa89 said:
No, i don't know what the right side means.
Actually I don' know what any of that means. Where did the 8 come from?
 
Elissa89 said:
No, i don't know what the right side means.

- - - Updated - - -Actually I don' know what any of that means. Where did the 8 come from?

You haven't studied Euler's formula? How about de Moivre's theorem?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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