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1. Contour integral of a square-root branch ●●●○○ 50 ptsLet $C$ be the circle $|z|=R$ with $R>1$, centred at the origin. Use the branch of $(z^2-1)^{1/2}$ with a straight branch cut joining $z=-1$ and $z=1$, chosen so that $(z^2-1)^{1/2}>0$ for real $x>1$. Let $I=\oint_C (z^2-1)^{1/2}\,dz$, taken counterclockwise. Write $I=b\,i$ with $b$ real. Find $b$, rounded to two decimal places.