I see. I was worrying whether the textbook was misprinted. Other mathematical physics book says the domain of the single-valued function is F(z) = ln(z) = ln(r) + iθ is α ≤ θ < α + 2π.
I think my book was misprinted:)
Let's have any non-zero complex number z = reiθ (r > 0) and natural log ln applies to z.
ln(z) = ln(r) + iθ. In fact, there is an infinite number of values of θ satistying z = reiθ such as θ = Θ + 2πn where n is any integer and Θ is the value of θ satisfying z = reiθ in a domain of -π <...