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\textbf{Math 425: Complex Variables}
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\textbf{Quiz 9}\quad \textsl{April 19, 2002}

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Let $p(z) = z^9 + 2z^5 + 4z^3 + 9$.

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1. Use Rouch\'e's Theorem to count the number of zeros of $p$ in the
annulus $1 < |z| < 2$.

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2. Use the Argument Principle to count the number of zeros of $p$
in the first quadrant.

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\emph{Bonus:} Deduce how many zeros are in each quadrant and how many are
on the axes (only elementary arguments are needed).


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