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\textbf{Math 425: Complex Variables}
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\textbf{Quiz 2}\quad \textsl{February 1, 2002}

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1. Let $f(z) = \frac{z^3+i}{z-i}$ for $z \ne i$. Determine the value
that should be assigned to $f(i)$ so that $f(z)$ is continuous at $z = i$.

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2. Find the limit of the sequence $z_n = \Big(\frac{1+i}{2}\Big)^n$, if it
converges, or explain why it diverges.

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3. Compute the sum of the infinite series $\sum_{n=0}^\infty\frac{2^n
+ i^n}{3^n}$.

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