# complex plane

we are given that $u_n$ (n is greater than or equal to 0)converges normally on E, a subset of C, the complex plane (converging normally means that the series of $llull$ for n greater than or equal to 0 converges, where llull=sup lu(z)l (where z is an element of E), is the sup-norm of u. i need to show the following:
1. for each z in E, the series $u_n(z)$ (n greater than or equal to 0) of complex numbers, converges. denote the sum by v(z)= $u_n(z)$ (n greater than or equal to 0).
2. the series $u_n(z)$ (for n greater than or equal to 0) converges to v(z) uniformly on E.