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{\bf Question}
\begin{itemize}
\item[a)]
Evaluate the sum of the series
$$\sum_{n=-\infty}^\infty\frac{1}{(2n-1)^2}$$
You should justify the steps in your method, except that you may
assume without proof inequalities relating to the function
$\cot\pi z$.
\item[b)]
State Rouche's theorem and use it to show that all the roots of
the equation
$$z^7+(1-i)z^5+2z^3-1=0$$
lie in the annulus $\frac{1}{2}\leq|z|<2$. Find a value of $k$
smaller than 2 with the property that all the roots of the
equation satisfy $|z|