While computing this integral $\displaystyle \int_{-1}^{1}\frac{dx}{\sqrt{1-x^2})}$, I am having trouble at finding residue at -i. My work is like this $\displaystyle a_{-1}(-i)=\frac{1}{\sqrt{2}.2e^{i3\pi/2}}$, but there is mistake in here and I haven't been able to figure it out.