Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2018 • Question 8

Question

Math 6210 • Real Analysis Summer 2018 • Question 8

Let \(f:\mathbb H\to \mathbb D\) be a bijective holomorphic map. Are we guaranteed that \[ -f(\bar z)=-\overline {f(z)}? \] In words, is negative \(f\) at the conjugate input equal to the negative complex conjugate of the original output?

Raw LaTeX

Let \(f:\mathbb H\to\mathbb D\) be a bijective holomorphic map.
Are we guaranteed that
\[
-f(\bar z)=-\overline{f(z)}?
\]
In words, is negative \(f\) at the conjugate input equal to the negative
complex conjugate of the original output?

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Zeros of Holomorphic Functions and the Identity Theorem