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

## Homework Statement

The problem along with its solution are attached as TheProblemAndSolution.jpg. This post's focus is on part (iii), specifically.

## Homework Equations

z (overlined) = z. (according to book)
z (double overlined) = z. (according to me)

## 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!

#### Attachments

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

jedishrfu
Mentor
I can't see your jpg TheProblemAndSolution.jpg

jedishrfu:
Sorry, I forgot to attach the picture.

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

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

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

Dick
Homework Helper
jedishrfu:
Sorry, I forgot to attach the picture.

Dick:
z = a + bi (which is complex and not solely real) in the problem.
By z is real, I just mean b=0 in z=a+bi.

Sorry for the triple post.

Look two posts down.

Sorry for the triple post.

Look one post down.

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. :)

Dick
Homework Helper
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. :)
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.

jedishrfu
Mentor
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.
Yes, it was named in honor of Bar Rafaeli:

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

Dick
Homework Helper
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. :)

Dick
Homework Helper
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. :)
Sure, joke. You're welcome!

CompuChip
Homework Helper
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.

Dick
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.