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Math Help - help with exp

  1. #1
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    help with exp

    can someone please show me how

    exp(.5ln(3e^(i*theta))
    is

    exp(.5(ln3+i*theta))

    i thought e^(ab) was not equal to e^a times e^b

    rather e^(a+b) was e^a times e^b

    thnks
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  2. #2
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    Quote Originally Posted by mpl06c View Post
    can someone please show me how

    exp(.5ln(3e^(i*theta))
    is

    exp(.5(ln3+i*theta))

    i thought e^(ab) was not equal to e^a times e^b

    rather e^(a+b) was e^a times e^b

    thnks


    It's just the definition of the complex natural logarithm Ln\,z , with \ln|z| the usual real natural logarithm:

    for z\in\mathbb{C}\,,\,\,Ln\, z:=\ln|z|+i\arg(z) , so:

    Ln\left(3e^{i\theta}\right)=\ln 3+i\theta ...


    Tonio
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  3. #3
    Member mabruka's Avatar
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  4. #4
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    Quote Originally Posted by mpl06c View Post
    can someone please show me how

    exp(.5ln(3e^(i*theta))
    is

    exp(.5(ln3+i*theta))

    i thought e^(ab) was not equal to e^a times e^b

    rather e^(a+b) was e^a times e^b

    thnks
    Yes, but ln(ab)= ln(a)+ ln(b) and that is what is being used.

    ln(3e^(i*theta))= ln(3)+ ln(e^(i*theta))= ln(3)+ i*theta.
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