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

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Discussion Overview

The discussion revolves around finding the square roots of the complex number \(4\sqrt{3} + 4i\). Participants express confusion regarding the question's wording and the mathematical concepts involved, including Euler's formula and de Moivre's theorem.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the question from a study guide, questioning whether it was taught by their professor.
  • Another participant proposes a transformation of the complex number into polar form, suggesting \(y=8\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)=8e^{\frac{\pi}{6}i}\) but does not explain the derivation of the factor of 8.
  • A participant indicates a lack of understanding of the proposed transformation and asks for clarification on the meaning of the right side of the equation.
  • There is a mention of Euler's formula and de Moivre's theorem, implying that these concepts may be necessary for understanding the problem, but no further explanation is provided.

Areas of Agreement / Disagreement

Participants do not appear to agree on the understanding of the mathematical concepts involved, and there is a lack of consensus on how to proceed with the problem.

Contextual Notes

There are missing assumptions regarding the participants' familiarity with complex numbers, polar coordinates, and relevant mathematical theorems, which may affect their ability to engage with the problem.

Elissa89
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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?
 

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