Let $V$ be a complex vector space of dimension $1$. Let $||.||$ be a norm on $V$ and let us note $C_R$ the circle of center $0$ and radius $R$ associated to this norm. ($R>0.$) Let $dz$ be a Haar measure on $V$.
Are we sure that $$\int_{C_R} dz = cR$$ for some real constant $c$ (which does not depend on $R$) ?