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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2023 • Question 4

Question

Math 6220 • Complex Analysis Fall 2023 • Question 4

Recall that the hyperbolic metric on \(\mathbb {H}\) is given by

\[ ds^2=\frac {dx^2+dy^2}{y^2} \]

Compute the hyperbolic distance between \(i\) and \(1+i\).

Raw LaTeX

Recall that the hyperbolic metric on \(\mathbb{H}\) is given by

\[
ds^2=\frac{dx^2+dy^2}{y^2}
\]

Compute the hyperbolic distance between \(i\) and \(1+i\).

Topic Tags

Hyperbolic Geometry in the Disk and Half-Plane