-.733448502640020+0.*I

i am investigating above numeric

when ln(-.733448502640020+0.*I);

-.3099978916+3.141592654*I

it has Pi imaginary part

then

i try

complex(1, exp(Pi)^3);

it return Complex(...) but not 1 + i*exp(Pi)^3

3 means 3 times come from recursively using pattern ln(Re(ln(x) - 3.141592654*I))

3.141592654 in imaginary part appear 3 times

i use Round(Im(x), 8) during above operation

actually i want to extract Pi imaginary part from -.733448502640020+0.*I

however, after minus exp(Pi) from it first time,

it is near the original number -.733448502640020

is this elimination of imaginary part is just a illusion from log function?