Complexities of Logarithm

Discussion in 'Other Advanced Math' started by etbassoon, Mar 31, 2022.

  1. etbassoon

    etbassoon

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    I have two questions about complex logarithms.

    First
    (-3)^3 = -27, but in Mathematica I get Log[-3,-27]=(i pi + Log[27])/(i pi + Log[3]) instead of 3.

    Second
    Ln(x+iy) = Ln[sqrt(x^2+y^2)] + i arg(x+iy), so that implies that for x>1, Ln(x^i) = i Ln(x) , Ln|x^i|=0 and arg(x^i)= Ln(x) which does not sit well with me.

    Any thoughts?
     
    etbassoon, Mar 31, 2022
    #1
  2. etbassoon

    etbassoon

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    etbassoon, Mar 31, 2022
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