I have reached a step in the question where I have to apply the Cauchy Riemann formulas to:

How would I apply the Cauchy Riemann formula to answer the rest of the question?

And how would I know if it is analytic?

The cauchy-riemann formula:

The function f(z)= g(x,y)+ h(x,y)i is differentiable with respect to z= x+ iy only if it satisfies the "Cauchy-Riemann equations":

and