please help me
Please show work attempting to the problem.
I want the understanding of way that led us to this result
@m s a: yeah.. we get that.. and what we need is that you show that you've solved something in this problem.. or atleast made an effort in this direction.
If I was knowing the way to what asked
According to the Physics Forums Global Guidelines you are required to show an attempt or detail your thoughts on a homework question before we can provide assistance.
You just have some idea how to prove the identity or else you wouldn't have been asked to prove it.
m_s_a, if you are really blocked, tell us the relation between log and exp, and then reflect on it.
Things would go much faster if you could convey simple information in some other way besides .bmp attachments. Those have to be approved before anyone can see them.
m_s_a, can you write a general complex number, z, in exponential form?
So you are saying
If y= ln(z) then z= ey
Now, if y= a+ bi, what is ey?
(and remember that ep+q= epeq)
I came to this result then do it is right or no ?
Is there some reason why you insist upon posting attachments after you have been told its a bad idea?
It's not all that difficult to type:
(this would look much nicer in LaTex but I have typed it in ASCII)
z= |z|e^(i theta)
ln z= ln |z| e^(i theta) (Well, ln z= ln(z e^(i theta)) is correct)
ln z= ln |z|+ ln(e^i theta)
ln z= ln |z|+ i ln(theta)
i.e. log(z)= ln z
Assuming that your textbook has specified a convention that natural logarithm applied to complex numbers will be designated by "log", which is implied by the question itself, then it is not correct to write "ln z". Other than that, what you wrote is correct.
Separate names with a comma.