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3 years ago in Computational Geometry , Mathematics By Rajshree Tamang

How can the logarithm of negative numbers be taken in computations?

Standard software libraries throw domain errors for negative inputs. I understand there’s a complex solution, but I need to know the precise formula and, more importantly, how to implement it correctly in code without losing physical meaning.

MATLAB ComplexLogarithm Negative number

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By Sumitra R Answered 1 year ago

In computational applications, this requires direct handling. For a negative real number −x (with x > 0), the natural logarithm under the principal branch is defined as ln(−x) = ln(x) + iπ, since −x = x ⋅ e^(iπ). In practice, you must use libraries that handle complex numbers for example, in Python, cmath.log() rather than math.log(). A key consideration is branch selection: the +iπ result follows from the principal branch (−π, π]. When computations repeatedly cross the negative real axis, careful management of branch cuts becomes necessary to maintain continuity a step I have found critical for accuracy in iterative solvers.

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