# Complex Analysis problem

## Homework Statement

Let f and g be two holomorphic functions in a connected open set D of the plane which have no zeros in D; if there is a sequence an of points such that lim an = a and an does not equal a for all n, and if

f'(an)/f(an)=g'(an)/g(an)

show that there is a constant c such that f=cg in D.

## Homework Equations

If f is identically zero at a point in a connected open set, then f is identically zero on the whole set.

## The Attempt at a Solution

I have shown that (f/g)'(a) = 0, but I don't see how that would imply that the derivative is identically zero at that point.

Last edited:

HallsofIvy