Question 42
For each complex $z$ define $A_z = \{1+z+z^2+\dots+z^n \mid n \in \mathbb{N}\}$.
a) Find all $z$ for which $A_z$ is finite.
b) How many complex numbers $z$ have the property that $A_z$ has 2013 elements?
a) Find all $z$ for which $A_z$ is finite.
b) How many complex numbers $z$ have the property that $A_z$ has 2013 elements?