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

[robertjford80]

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.

 

[scurty]

$\mathbb{R} \subseteq \mathbb{C}$

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.

 

[SteveL27]

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.

 

[robertjford80]

thanks, I did feel tricked, but I get the point now.