if z=(3+7i)(p+iq),where p,q are non-zero integers,is purely imaginary then minimum value of |z|^2 is

z=(3+7i) (p+iq)=(3p-7q)+i(3q+7p)
now it is said z is purely imaginary
so,
3p-7q=0
or p/q=7/3
or p/q + i = 7/3 +i
(p+qi)/q=7+3i/3
from here the p+iq = 7+3i

z= 58i
|z²|= 3364