What are the five values of (1+i√3)^(3/5)?

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Homework Help Overview

The problem involves finding the five values of the expression (1+i√3)^(3/5), which is related to complex numbers and their roots. The original poster expresses uncertainty about the nature of the question, particularly whether it involves finding the five roots of the expression.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Some participants clarify that the task is to find the five fifth roots of (1+i√3) raised to the third power. Others mention applying D'Moivre's theorem to the expression, indicating different approaches to the problem.

Discussion Status

The discussion is exploring various interpretations of the problem, with participants providing insights into the nature of the expression and its roots. There is a recognition of the relationship between the expression and the value -8, which has prompted further questions about its implications.

Contextual Notes

Participants note the surprising equivalence of the third power of the expression to -8, which raises questions about the nature of complex numbers and their real counterparts. There is also a mention of potential reluctance to equate the expression with a real number.

juliany
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Homework Statement


Find the five values of (1+i√3)^(3/5)

This question was from my recent end of year exam, I hadn't come across a question like it in my revision, does it mean find the five roots of (1+i√3)^(3/5) ?:confused:
 
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You want to find the five 5th roots of (1+i√3)3.
 
you want to find all the solutions of the equation X5 = (1 + i√3)3 = -8.
 
It's remarkable that the third power is equal to -8!

Yes, you can find the five fifth roots of [itex](1+i\sqrt{3})^3[/itex] or just apply D'Moivre's theorem to [itex]1+ i\sqrt{3}[/itex] with n= 3/5.
 
It's remarkable that the third power is equal to -8!

why?
 
Because it's a real number. (-2)3=-8 as well so some might be reluctant enough to say that [tex]1+i\sqrt{3}=-2[/tex] :-p
 

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