# Thread: complex in the form a+ib

1. ## 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.

2. ## Re: complex in the form a+ib

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 $\displaystyle \ln{\left( 1 + e^i \right)}$ in the form $\displaystyle a + b\,i$?

3. ## Re: complex in the form a+ib

Hint :

$e^{ix}=\cos(x)+i\sin(x)$

4. ## Re: complex in the form a+ib

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

5. ## 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.

6. ## Re: complex in the form a+ib

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 ?

Correct

8. ## Re: complex in the form a+ib

Originally Posted by Prove It
Correct
thanks alot.

9. ## Re: complex in the form a+ib

Originally Posted by sigma1
thanks alot.

The Alot says "You're Welcome"