Question 15
Let $i=\sqrt{-1}.$ For $n\ge1,$ define a sequence of complex numbers by $$
\begin{aligned} z_1&=0,\\ z_{n+1}&=z_n^2+i. \end{aligned}
$$ In the complex plane, how far from the origin is $z_{111}?$
\begin{aligned} z_1&=0,\\ z_{n+1}&=z_n^2+i. \end{aligned}
$$ In the complex plane, how far from the origin is $z_{111}?$