## Translation of a polynomial

I am given a complex polynomial p(z) = a_0 + a_1z + \cdots + a_nz^n, with a_j \in \Bbb C for all j. Then, we fix z_0 \in \Bbb C and define P(z) = p(z+z_0), and I must prove that P is also a polynomial. By doing some examples, comparing with the Pascal triangle, doing … Read more