Let $$z=x+iy$$ where $$i = \sqrt { - 1} .$$ Then $$\overline {\cos \,z} = $$

The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$
where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$$ in the complex plane is ____.

In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form
$$f\left( z \right) = 1 + \left( {1 - z} \right) + {\left( {1 - z} \right)^2} + ..................$$
Then $$f(z)$$ is

The value of $$\oint\limits_c {{1 \over {{z^2}}}dz} $$ where the contour is the unit circle traversed clock - wise, is