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\textbf{Math 425: Complex Variables}
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\textbf{Quiz 5}\quad \textsl{March 1, 2002}

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1. Define the radius of convergence of a complex power series
$\sum_{n=0}^\infty a_n(z-z_0)^n$.

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2. Find the radius of convergence of the power series $\sum_{n=0}^\infty
\frac{z^{3n}}{1+4^n} = \frac{1}{2} + \frac{z^3}{5} +\frac{z^6}{17} + \cdots$.

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3. Find the power series about the origin for $f(z) = \frac{1+z^2}{1-z^2}$.

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