Let f(z) be analytic in a region R bounded by two concentric circles C1 and C2 and on the bounda

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Step 1:  u000ARecall the Cauchy Integral Formula, which states that if u005C( f(z) u005C) is analytic inside

Let $f(z)$ be analytic in a region $R$ bounded by two concentric circles $C_1$ and $C_2$ and on the boundary [Fig. 5-11]. Prove that if $z_0$ is any point in $R$, then $$ f\left(z_0\right)=\frac{1}{2 \pi i} \oint_{C_1} \frac{f(z)}{z-z_0} d z-\frac{1}{2 \pi i} \oint_{C_2} \frac{f(z)}{z-z_0} d z $$