AOPS Algebra formatting question for roots of quadratics

[Sebastian (a lady)]

Can someone give me insight on why answers to quadratic roots are formatted in the Intro to Algebra book different ways in different problems.

 

Ex.  13.2.1 b  has both the real and imaginary part of the root written as separate fractions with a denominator of 2.

 

I can see that this can have advantages like in problem 13.2.1 f where the real portion of the root can be simplified.

 

BUT why is the answer to 13.3.1 b written as a single fraction?  I thought that this might be the practice when working with an imaginary number as part of the root (as in 13.3.1 d and f) but I'm not seeing a consistent practice across the answers.

 

It would seem that the answers are equivalent whether written as the sum of two fractions or as a single fraction.  Is there a reason for one format over the other?

[Sebastian (a lady)]

Anyone?

[daijobu]

Hi:  I'm looking at the answer to 13.3.1(b) and it looks like the answer is a real number, all written as one fraction.  It is not a complex number with separate real and imaginary components.  It looks like the solution was derived from the quadratic formula, which is a single fraction, so it just seemed logical to keep it as a fraction.  

 

I think generally if the answer is real, you keep it as a single fraction.  If it's complex, you can separate the real and imaginary parts for clarity, but I don't think that's even necessary, as you see in 13.3.1 (d, f)

 

When you get to graphing complex numbers or doing operations on them (adding, multiplying, taking the conjugate), it helps to have the real and imaginary components separate.  But as you see in 13.3.1 (d,f) it's a simple thing to take one additional step.  

 

Does that help?  

[Sebastian (a lady)]

It does. Perhaps the difference is that one group of problems were solved with completing the square while the other set used the quadratic formula. So maybe process used is driving the formatting of the solution.