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\textbf{Math 425: Complex Variables}
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\textbf{Quiz 3}\quad \textsl{February 8, 2002}

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1. Define $e^z$ for a complex number~$z$ and show that $e^z e^w = e^{z+w}$.

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2. Define $\cos(z)$ and $\sin(z)$ for a complex number~$z$ and show that
$\sin^2(z) + \cos^2(z) = 1$.

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3. Find the real and imaginary parts of $\log(-3)$ and $(-1+i)^{2i}$.

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