Complex number proof about z (single or double overlined/conjugate) = z.

1. Jan 30, 2013

s3a

1. The problem statement, all variables and given/known data
The problem along with its solution are attached as TheProblemAndSolution.jpg. This post's focus is on part (iii), specifically.

2. Relevant equations
z (overlined) = z. (according to book)
z (double overlined) = z. (according to me)

3. The attempt at a solution
I understand the first two parts but, is there a typo in part (iii)? I looked at Wikipedia and I believe that part (iii) intends to say double conjugate of z = z rather than single conjugate of z = z. Am I right in believing that the book I'm using is wrong?

I would really appreciate a confirmation or denial because, I want to make sure that I am not missing something important if I just assume that the book is wrong!

Attached Files:

• TheProblemAndSolution.jpg
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Last edited: Jan 30, 2013
2. Jan 30, 2013

Dick

$\bar{z}=z$ only if z is real. $\bar{\bar{z}}=z$ for any z.

3. Jan 30, 2013

Staff: Mentor

I can't see your jpg TheProblemAndSolution.jpg

4. Jan 30, 2013

s3a

jedishrfu:
Sorry, I forgot to attach the picture.

Dick:
z = a + bi (which is complex and not solely real) in the problem.

5. Jan 30, 2013

Staff: Mentor

Yeah, it looks like the book is wrong for iii.

z=a + bi so zbar = a - bi zbarbar = a + bi hence zbarbar = z

6. Jan 30, 2013

Dick

By z is real, I just mean b=0 in z=a+bi.

7. Jan 30, 2013

s3a

Sorry for the triple post.

Look two posts down.

8. Jan 30, 2013

s3a

Sorry for the triple post.

Look one post down.

9. Jan 30, 2013

s3a

Okay so, what the book most likely wanted to ask was: "Prove that z = z (double overlined)."?

[Technically, I believe the term "bar" is incorrect since, looking at h-bar (Planck's constant divided by (2*pi)), I believe that the bar is always through the letter and not above it.]

Edit:
Dick:
Yes, I know. :)

10. Jan 30, 2013

Dick

Yes, I think the book wants you to prove $\bar{\bar{z}}=z$. It's just a typo. And lots of people say 'bar' when they see the symbol. The pronunciation is not that formalized.

11. Jan 30, 2013

Staff: Mentor

Yes, it was named in honor of Bar Rafaeli:

http://en.wikipedia.org/wiki/Bar_Refaeli

12. Jan 30, 2013

Dick

13. Jan 30, 2013

s3a

Wait, is that a joke or something?

I ask because that woman is pretty young and I'm not sure but, wasn't that notation available to physicists that lived before she was born?

Edit:
Also, about the main focus of this thread.: Thank you both. :)

14. Jan 30, 2013

Dick

Sure, joke. You're welcome!

15. Jan 30, 2013

CompuChip

I was staring at the proof in your attachment, maybe I'm just dumb at the moment but it really looks like an (incomprehensible) proof for $\overline{z} = z$ ... it's not like the just made a typo with the bars.

16. Jan 30, 2013

Dick

You're right. I didn't even look at the 'proof'. Pretty incoherent. I'm sure s3a will do better.

17. Jan 30, 2013

Staff: Mentor

Many times these errors creep into problem sets as they edit the problem to make it tougher. Looking at it though I couldn't quite reconstruct what the earlier problem wanted proven. It may have been given z= zbar to demonstrate b=0.