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Math Help - complex in the form a+ib

  1. #1
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    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.
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  2. #2
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    Re: complex in the form a+ib

    Quote Originally Posted by sigma1 View Post
    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 ?
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  3. #3
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    Re: complex in the form a+ib

    Hint :

    e^{ix}=\cos(x)+i\sin(x)
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  4. #4
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    Re: complex in the form a+ib

    Quote Originally Posted by Prove It View Post
    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 .
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  5. #5
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    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.
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    Re: complex in the form a+ib

    Quote Originally Posted by Prove It View Post
    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.
    so the answer would be

    cos1 + isin1 ?
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  7. #7
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    Re: complex in the form a+ib

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

    Quote Originally Posted by Prove It View Post
    Correct
    thanks alot.
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  9. #9
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    Re: complex in the form a+ib

    Quote Originally Posted by sigma1 View Post
    thanks alot.


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