complex in the form a+ib

• Mar 15th 2013, 07:33 PM
sigma1
complex in the form a+ib
hello all, i have the following question which i am trying to solve. express ln1+ e^i in the form a + ib.

what i have done.

ln both sides therefore

i = ln (a+ib)
i= ln a + ln ib

equating real and imaginary parts

ln a = 0
a= 1

and

i = ln ib
1= ln b

b= e

ans= 1+ie

is this correct? if not how would i appraoch the problem. thanks.
• Mar 15th 2013, 08:51 PM
Prove It
Re: complex in the form a+ib
Quote:

Originally Posted by sigma1
hello all, i have the following question which i am trying to solve. express ln1+ e^i in the form a + ib.

what i have done.

ln both sides therefore

i = ln (a+ib)
i= ln a + ln ib

equating real and imaginary parts

ln a = 0
a= 1

and

i = ln ib
1= ln b

b= e

ans= 1+ie

is this correct? if not how would i appraoch the problem. thanks.

Some brackets would be nice. Are you asking to write $\displaystyle \displaystyle \ln{\left( 1 + e^i \right)}$ in the form $\displaystyle \displaystyle a + b\,i$?
• Mar 15th 2013, 09:27 PM
princeps
Re: complex in the form a+ib
Hint :

$\displaystyle e^{ix}=\cos(x)+i\sin(x)$
• Mar 16th 2013, 02:36 PM
sigma1
Re: complex in the form a+ib
Quote:

Originally Posted by Prove It
Some brackets would be nice. Are you asking to write $\displaystyle \displaystyle \ln{\left( 1 + e^i \right)}$ in the form $\displaystyle \displaystyle a + b\,i$?

well the question does not have any brackets in it. am wondering if its an error. but how would you attempt to solve it without the brackets. that is ln1 + e^i .
• Mar 16th 2013, 03:03 PM
Prove It
Re: complex in the form a+ib
Well ln(1) = 0, so you're really just trying to simplify e^i, or if you like, e^(1i). Use the hint Princeps gave you.
• Mar 16th 2013, 05:37 PM
sigma1
Re: complex in the form a+ib
Quote:

Originally Posted by Prove It
Well ln(1) = 0, so you're really just trying to simplify e^i, or if you like, e^(1i). Use the hint Princeps gave you.

cos1 + isin1 ?
• Mar 16th 2013, 05:38 PM
Prove It
Re: complex in the form a+ib
Correct
• Mar 16th 2013, 05:45 PM
sigma1
Re: complex in the form a+ib
Quote:

Originally Posted by Prove It
Correct

thanks alot.
• Mar 16th 2013, 07:21 PM
Prove It
Re: complex in the form a+ib
Quote:

Originally Posted by sigma1
thanks alot.

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