From the first equality we can for instance conclude that when the variation of the argument of f (iy) is positive, then f (z) will have more roots to the left of the imaginary axis than to its right. The equality p − q = w (+∞) − w (−∞) can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is p + q and the w from the right member is the number of variations of a Sturm chain (while w refers to a generalized Sturm chain in the present theorem).