What is the Nature of the Solution to x^2 = 1?

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Homework Help Overview

The discussion revolves around the equation x2 = 1, with participants exploring the nature of its solutions in terms of being real, complex, or imaginary.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the solutions x = ±1 and question the classification of these solutions as both real and complex. There is an exploration of the definitions of complex numbers and the implications of real numbers being a subset of complex numbers.

Discussion Status

Some participants express confusion regarding the classification of the solutions, noting that while they agree with the solution, the terminology used in the textbook seems misleading. There is acknowledgment of the underlying concept that real numbers can also be considered complex numbers.

Contextual Notes

Participants mention feeling misled by the question's phrasing, indicating a potential ambiguity in how the terms "real" and "complex" are presented in the context of the problem.

robertjford80
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Homework Statement



solve the following and determine if it is complex, real and/or imaginary

x2 = 1



The Attempt at a Solution



The answer is x = +-1 which I agree with but the book says that that is complex and real. How complex? Complex numbers have the form a + bi, there's no bi in that answer.
 
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##\mathbb{R} \subseteq \mathbb{C}##

A complex number ##c## can represented as ##c = a + bi## where ##a,b \in \mathbb{R}##

In this case, b=0. A purely imaginary number is when a=0.
 
robertjford80 said:

Homework Statement



solve the following and determine if it is complex, real and/or imaginary

x2 = 1



The Attempt at a Solution



The answer is x = +-1 which I agree with but the book says that that is complex and real. How complex? Complex numbers have the form a + bi, there's no bi in that answer.

They're trying to get you to see that real numbers are complex numbers. But it's a little misleading, since clearly if someone asks if 1 is "real or complex," the answer is real ... even though technically, the right answer is "both." I think this is a bit of a trick question.
 
thanks, I did feel tricked, but I get the point now.
 

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