# Find ln z?

• Mar 24th 2013, 06:08 AM
szak1592
Find ln z?
ln z = ln (mod of z) + i Arg z +- (2n pi) i

ln (e3i )
• Mar 24th 2013, 06:25 AM
Prove It
Re: Find ln z?
Can't you immediately read off what $\displaystyle \left| e^{3i} \right|$ and $\displaystyle \arg{\left( e^{3i} \right)}$ are?
• Mar 24th 2013, 06:34 AM
szak1592
Re: Find ln z?
I can get the mod but i dont how to find the Arg of e^3i, please teach me how to find the Arg of this kinda function
• Mar 24th 2013, 09:29 AM
Plato
Re: Find ln z?
Quote:

Originally Posted by szak1592
I can get the mod but i dont how to find the Arg of e^3i, please teach me how to find the Arg of this kinda function

$e^z=e^{x+yi}=e^x[\cos(y)+i\sin(y)]$ so $\text{arg}(e^z)=~?$
• Mar 24th 2013, 04:03 PM
Prove It
Re: Find ln z?
Quote:

Originally Posted by szak1592
I can get the mod but i dont how to find the Arg of e^3i, please teach me how to find the Arg of this kinda function

Surely you can see it's written as $\displaystyle e^{\theta i}$. What is $\displaystyle \theta$?
• Mar 25th 2013, 01:51 AM
szak1592
Re: Find ln z?
okay it is 3, so cos 3 + i sin 3 so it means arg z = arc tan of sin3/cos3, rite???
• Mar 25th 2013, 01:55 AM
Prove It
Re: Find ln z?

Of course if you were going to do it your way, you'd note that sin(x)/cos(x) = tan(x) and so your arctangent cancels off anyway.
• Mar 25th 2013, 11:09 AM
SworD
Re: Find ln z?
Quote:

ln (e3i )
You should have noticed that the ln and e^ functions are inverses of each other, so in at least some branch, ln(e^(z)) = z. Then think about what the angle/magnitude of this would be, whether this result makes sense and if not, what you need to do to make it make sense.