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⋅e^{iθ}, 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

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