Suppose functions f and g are analytic at x0 Prove that fg i

Suppose functions f and g are analytic at x0. Prove that f*g is analytic at x0.

Solution

We know that if the functions f and g are differentiable at z₀ then f+g,f-g,fg are all differentiable at z₀ if a function is differentiable and satisfies necessary conditions i.e cauchy reimann equations then f* g is analytic at x_0.