Question 77
Let $x$ and $y$ be complex numbers such that $|x|=|y|=1$.
a. Determine the maximum value of $|1+x|+|1+y|-|1+xy|$.
b. Determine the maximum value of $|1+x|+|1+xy|+|1+xy^{2}|+\ldots+|1+xy^{2011}|-1006|1+y|$.
a. Determine the maximum value of $|1+x|+|1+y|-|1+xy|$.
b. Determine the maximum value of $|1+x|+|1+xy|+|1+xy^{2}|+\ldots+|1+xy^{2011}|-1006|1+y|$.