Complex Signum
The signum function can be generalized to complex numbers as
for any z ∈ except z = 0. The signum of a given complex number z is the point on the unit circle of the complex plane that is nearest to z. Then, for z ≠ 0,
where arg is the complex argument function. For reasons of symmetry, and to keep this a proper generalization of the signum function on the reals, also in the complex domain one usually defines, for z = 0:
Another generalization of the sign function for real and complex expressions is csgn, which is defined as:
where is the real part of z, is the imaginary part of z.
We then have (except for z = 0):
Read more about this topic: Sign Function
Famous quotes containing the word complex:
“All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.”
—Terry Eagleton (b. 1943)