Use the Cauchy-Riemann equations to show that the function $g(z) = \sin (\bar z)$ is not analytic at any point of $\mathbb{C}$.
Here's as far as I got -
$\sin \left(\frac{\bar z}{1}.\frac{z}{z}\right) =\sin \left(\frac{|z|^2}{z}\right) =\sin \left(\frac{x^2 + y^2}{x+iy}\right)$
I can't see how to separate the real and imaginary parts so that I can apply the Cauchy-Riemann equations.