What is the Use of deMoivre's Formula in Finding Roots of Complex Numbers?

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Discussion Overview

The discussion revolves around the application of de Moivre's formula in finding the roots of complex numbers, specifically in relation to the square root of -i. Participants explore the mathematical implications and methods involved in this process.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks about the square root of -i, prompting others to clarify the notation and approach.
  • Another participant suggests that the expression -i can be represented in exponential form, indicating a method to find its roots.
  • There is a reference to the identity e^(ix) = cos x + i sin x, which is relevant to the discussion of complex numbers.
  • One participant expresses skepticism about the applicability of de Moivre's theorem for this problem, questioning its effectiveness.
  • In response, another participant asserts that de Moivre's theorem can indeed be used to find any root of any complex number, emphasizing its relevance.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the effectiveness of de Moivre's theorem in solving the problem, with some supporting its use while others remain skeptical.

Contextual Notes

Some assumptions about the definitions and properties of complex numbers and their roots may not be explicitly stated, leading to potential gaps in understanding the application of de Moivre's theorem.

Who May Find This Useful

Readers interested in complex analysis, mathematical methods for solving equations, and the application of theorems in complex number theory may find this discussion relevant.

mohamen
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wat is under root - i ?

please anser this
 
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Do you mean [itex]\sqrt{-i}[/itex]? You can figure it out yourself! If [itex]a + bi = \sqrt{-i}[/itex], then what does the definition of square root tell you?
 
HINT:

[tex]-i=e^{-\frac{i\pi}{2}+2k\pi} , \ k\in\mathbb{Z}[/tex]

Daniel.
 
Hey guys, don't post here often, i will more from now on. Anyway, dexter got that from the identity e^(ix)= cos x + i sin x.
 
will it be solved by the de mouvies theorem...i don't think so...
 
You mean "de Moivre". Yes, it will, since that theorem is a trivial consequence of the fact that

[tex]\left(e^{ix}\right)^{n}=e^{inx}[/tex]

Daniel.
 
mohamen said:
will it be solved by the de mouvies theorem...i don't think so...
I personally like Hurkyl's suggestion best but WHY don't you think deMoivre's formula will work? It can be used to find any root of any complex number.
 

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