Complex Logarithm - Applications

Applications

• The complex logarithm is needed to define exponentation in which the base is a complex number. Namely, if a and b are complex numbers with a ≠ 0, one can use the principal value to define ab = eb Log a. One can also replace Log a by other logarithms of a to obtain other values of ab.
• Since the mapping w = Log z transforms circles centered at 0 into vertical straight line segments, it is useful in engineering applications involving an annulus.