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    Complex Logarithms

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    3. Show that
    (a) Log (1 + i)2 = 2 Log (1 + i)

    (b) Log (-1 + i)2 ≠ 2 Log (-1 + i).

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    Solution Preview


    (1+i)= sqrt(2)*e^(i*Pi/4) ---> (1+i)^2=2*e^(i*Pi/2)

    The prinicpal arguments of both lie within -Pi and Pi.

    Log(1+i)^2= ln(2)+i(Pi/2+2n*Pi) (n=0,+-1, +-2...)
    Log(1+i)= ln(sqrt(2))+i(Pi/4+2m*Pi)= ...

    Solution Summary

    Complex Logarithms are investigated.