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Math Help - How do we natural log this?

  1. #1
    Senior Member
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    How do we natural log this?

     <br />
0.85((1+i)^2^0))<br />

    My attempt

     <br />
ln 0. 85 + 20ln(1+i)<br />
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by adam_leeds View Post
     <br />
0.85((1+i)^2^0))<br />

    My attempt

     <br />
\ln 0. 85 + 20\ln(1+i)<br />
    That is OK if we ignore the mismatched brackets in the statement of the problem.

    CB
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  3. #3
    MHF Contributor

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    You can continue by noting that 1+ i= \sqrt{2}e^{i\pi/2+ 2ik\pi} so that ln(1+ i)= ln(\sqrt{2})+ \pi/2+ 2k\pi for k any integer.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by HallsofIvy View Post
    You can continue by noting that 1+ i= \sqrt{2}e^{i\pi/2+ 2ik\pi} so that ln(1+ i)= ln(\sqrt{2})+ \pi/2+ 2k\pi for k any integer.
    For some reason it had not occured to me that the i was the imaginary unit!?

    CB
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