Question

A complex number is given by $Z_{n+1}=Z_{n}^2+i$
and $Z_{0}=0$
then distance of $Z_{111}$ from the origin is______

Answer 1

as
 $Z_{0}=0,Z_{1}=i,Z_{2}=1+i,Z_{3}=2+i,,Z_{4}=5+i,,\\Z_{5}=26+i,,Z_{6}=677+i..$
and so on
so u can find all  numbers and then at last when u get Z111 find its modulus 

Answer 2

Use the formula and find all the numbers till Z_{111} and then at last find its modulus 
and then square it u will get ur answer