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\textbf{Math 425: Complex Variables}
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\textbf{Quiz 7}\quad \textsl{March 22, 2002}

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1. Give the order of each of the zeros of $f(z) = z^2(1-\cos(z))$.

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2. \parbox[t]{6.25in}{Locate each of the isolated singularities of $f(z)
= \frac{e^z - 1}{e^{2z}-1}$ and determine whether it is a removable
singularity, a pole, or an essential singularity.}

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3. \parbox[t]{6.25in}{Suppose $f$ is an entire function and there is a
constant $c$ such that $\mathrm{Re} f(z) \le c$ for all~$z$. Show that
$f$ is constant. [Hint: Consider $\exp(f(z)$).]}

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