What is the natural logarithm of a negative number?
The natural logarithm function ln(x) is defined only for x>0.
So the natural logarithm of a negative number is undefined.
ln(x) is undefined for x ≤ 0
The complex logarithmic function Log(z) is defined for negative numbers too.
For z=r⋅eiθ, the complex logarithmic function:
Log(z) = ln(r) + iθ , r >0
So for real negative number θ = -π:
Log(z) = ln(r) - iπ , r >0