On pages 11-15 this rant goes off on a tangent about branch cuts in complex arithmetic. It distinguishes between C99-style complex numbers, which have a separate type for bare imaginary numbers, and Fortran-style complex numbers, which do not. The authors assert that it isn’t possible for Fortran-style complex numbers to handle signed zeroes correctly and therefore that programs written to use this style of arithmetic necessarily get branch cuts wrong.
This seems unlikely to me, if the programmer has suitable facilities for constructing or decomposing complex numbers from or into two reals. I guess they must be over-simplifying.