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Math Help - Complex number.. need an idea to start..

  1. #1
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    Complex number.. need an idea to start..

    1. The problem statement, all variables and given/known data

    Find the principal value of i^2i

    2. Relevant equations

    principal value = Ln r + iArg(z)

    3. The attempt at a solution
    dont know how to start..
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  2. #2
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    Quote Originally Posted by nameck View Post
    1. The problem statement, all variables and given/known data

    Find the principal value of i^2i

    2. Relevant equations

    principal value = Ln r + iArg(z)

    3. The attempt at a solution
    dont know how to start..
    Are you asking for the principle value of \ln(i^{2i})? If so it would be nice if you say so.

    (start by writing i in exponetial form: i=r e^{i\theta}, with r=1 and \theta = \pi/2 + 2n\pi)

    CB
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  3. #3
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    I think we are to find the principle value of i^{2i}.
    <br />
i^{2i}  = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?
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  4. #4
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    Yes Plato u are right..
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  5. #5
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    I dif that for you. Can you finish?
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  6. #6
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    Quote Originally Posted by Plato View Post
    I think we are to find the principle value of i^{2i}.
    <br />
i^{2i}  = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?
    how did u get pi/2?
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  7. #7
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    Quote Originally Posted by nameck View Post
    how did u get pi/2?
    The principle value of z^w=\exp\left(w\cdot\text{Log}(z)\right).
    Now \text{Arg}(i)=\frac{\pi}{2} and |i|=1 so \ln(1)=0
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  8. #8
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    Quote Originally Posted by Plato View Post
    I think we are to find the principle value of i^{2i}.
    <br />
i^{2i}  = \exp \left( {2i\text{Log}(i)} \right) = \exp \left( {(2i)\left( {i\frac{\pi }{2}} \right)} \right) = ?
    when did u insert Arg(z)?
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