Wednesday, Jan 18th

Problem
Prove that if $11z^{10}+10i z^9+10i z-11=0$ then $|z|=1$.

Solution
Suppose that $|z|>1$. Then $|z^{9}(11z+10i)|>|z|^9>|10i z -11|$. Similarly, if $|z|<1$ we have that $|z^{9}(11z+10i)|<|z|^9<|10i z -11|$. Thus $|z|=1$.