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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2023 • Question 3

Question

Math 6220 • Complex Analysis Fall 2023 • Question 3

Let \(P(z)\) be a nonzero polynomial. Show that the equation

\[ e^z=P(z) \]

has infinitely many solutions \(z\in \mathbb {C}\).

Raw LaTeX

Let \(P(z)\) be a nonzero polynomial. Show that the equation

\[
e^z=P(z)
\]


has infinitely many solutions \(z\in\mathbb{C}\).

Topic Tags

Zeros of Holomorphic Functions and the Identity Theorem