Yes, that’s the correct terminology for the specific fact that every polynomial of positive degree with complex coefficients has a root (and, a fortiori, factors uniquely into a product of a complex number and a number of monomials equal to its degree).
To be completely explicit:
Sure, the reals are complete in the senses of Dedekind or Cauchy whereas the rationals aren’t (and the complex numbers are Cauchy complete while it doesn’t make sense to apply the concept of Dedekind-completeness to them). Of course, there’s more than one use of the word “complete” in mathematics, and even moreso within ordinary language.
If you have two 2d vector quantities which start out equal (for convenience), with each rotating and scaling at their own constant rate (since we’re interested in exponential growth), with the velocity of the second quantity initially that of the first rotated 90 degrees (since the exponent we’re interested in is a 90 degree rotation), and after some time the first has cumulatively simply rotated 90 degrees from its initial value (since the base we’re interested in is a 90 degree rotation), then the second will have, in the same time, cumulatively simply have have multiplied its initial size by e[sup]-(z + 1/4)2π[/sup], where z is the integer number of full revolutions the first has gone through.
This being because, more generally, in this setup, the second vector never rotates, and whenever the first vector has rotated through d radians, the second vector will have decreased the natural logarithm of its size by d. And this is because the first vector must be simply rotating without scaling (as it has the same final size as initial size), so that its initial velocity is its initial value rotated 90 degrees and multiplied by some scalar, and thus the second vector’s initial velocity is its initial value rotated 180 degrees and multiplied by that same scalar, so that the second vector must be always scaling without rotating, and more specifically, with the natural logarithmic scaling rate of the second vector equal to the negation of the radian-measured rotation rate of the first vector, as stated.
…Well, perhaps that doesn’t help anyone. But it’s true.