The discussion focuses on finding the square roots of the complex number \(4\sqrt{3} + 4i\). A participant introduces the expression \(y = 8\left(\frac{\sqrt{3}}{2} + \frac{1}{2}i\right) = 8e^{\frac{\pi}{6}i}\) as a potential solution. However, confusion arises regarding the interpretation of this expression and the derivation of the coefficient 8. Key mathematical concepts mentioned include Euler's formula and de Moivre's theorem, which are essential for understanding the transformation of complex numbers.
PREREQUISITESStudents preparing for mathematics finals, particularly those studying complex numbers and their properties, as well as educators looking to clarify these concepts for their students.
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)
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?
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.
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?