Real & Imaginary Parts of Logarithms

[mkbh_10]

Homework Statement

Find the real & imaginary parts of log(1+i)log(i) ?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi mkbh_10!

What have you tried?

The first thing is to simplify the question, before answering it.

The only useful formula you know about log is loga + logb = logab.

Concentrate on just log(i), on its own.

How does that formula help you to simplify log(i)?

 

[mkbh_10]

(1+i) = (e)^i pi/4 , log(1+i)= i pi/4 & log(i) = i pi/2 , there product gives -(pi)^2/8 which is the principal value

 

[tiny-tim]

(btw, if you type alt-p, it prints π)

Yes, fine!

… except … slight mistake … (1+i) = (√2)(e)^iπ/4;

so log(1+i) = … ?

 

[mkbh_10]

tell me how to get these mathematical symbols , how to write an eqn like you have written ?

 

[mkbh_10]

log(1+i)= log(sqrt2)+log(e^i pi/4) = log(sqrt2)+ ipi/4= [1/2log(2)+i pi/4]*i pi/2


= i pi log(2)-(pi)^2/8

 

[tiny-tim]

… extra symbols on the keyboard …

= i pi log(2)-(pi)^2/8

erm … isn't it iπ log(2)/4 - π^2/8 ?

tell me how to get these mathematical symbols , how to write an eqn like you have written ?

On your keyboard, there should be a key marked alt or opt.

It's probably on the bottom row, next to the space-bar.

If it's not marked, just try each key which does nothing when you press it on its own.

Anyway, this key is like the shift key that types capitals for you - you hold down alt while you type a normal letter, and it gives you something different: `Ω≈ç√∫~µ≤≥÷«æ…¬˚∆˙©ƒ∂ßåœ∑´®†¥¨^øπ“‘≠–ºª•¶§∞¢#€¡

And if you press both the shift and the alt at the same time, you get ŸÛÙÇ◊ıˆ˜¯˘¿»ÆÚÒÔÓÌÏÎÍÅŒ„‰ÂÊÁËÈØ∏”’±—‚·°‡flfi›‹™⁄

Have you found it?

 

[mkbh_10]

Its not working like that

 

[tiny-tim]

Its not working like that

Do you mean that you can't find an alt key, or that you've found it but it doesn't do anything?

 

[mkbh_10]

it doesn't do nything

 

[tiny-tim]

ß ∂ ∆ µ π ∏ ∑ Ω … √ ∫ ≤ ≥ ≠ ± #

Hi mkbh_10!

I have a Mac, and the alt key gives all the symbols in my previous post.

But it looks as if the alt key on PC keyboards only operates the F1 etc function keys.

But surely PCs must have a way of typing these extra symbols?

I've been doing a bit of research in wikipedia.

I have two suggestions to try.

(1) Is there another alt key on the right-hand side of the space bar (it might be called alt-Gr)? If so, try that instead.

(2) Try pressing the control key and alt (and a letter) at the same time.

if neither of these work, I'll start a thread in the Lounge section to see if anyone else knows what to do!

Until then, or unless you want to buy a Mac, I suggest you save all the symbols from this thread into a separate document, and then copy and paste them whenever wanted.

Or just bookmark this thread, and copy direct from it!

For conveninence, I'll re-type the best ones here, for you to copy:

ß ∂ ∆ µ π ∏ ∑ Ω … √ ∫ ≤ ≥ ≠ ± #

 

[tiny-tim]

… see new thread …

Hi mkbh_10!

… if neither of these work, I'll start a thread in the Lounge section to see if anyone else knows what to do!

Done it … see

https://www.physicsforums.com/showthread.php?p=1654966 ​

So if you'd prefer the forum to supply these letters, join in the new thread and cast a vote for it!

 

[mkbh_10]

thnx