Is the set

a starlike set with star-centre 0?

I ask this because I need the result

, where [0,z] means the line segment from the star centre 0 to any point . Here f: is continuous and analytic on and so its integral around any closed path in C = 0, but only if C is starlike. So the integral around any triangular path in particular is equal to 0, which tels us we can differentiate the integral on C.

However I am not sure about C being starlike! Any help would be appreciated