Natural Logarithm of Negative Number

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


Natural logarithm of zero ►


See also

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