z=a+bi
x^2-ax+4+(3-bx)i=0
x^2-ax+4=0
3-bx=0
a=x+4/x
b=3/x
|z|=sqrt(a^2+b^2)
=sqrt(x^2+8+25/x^2)
=sqrt((x-5/x)^2+18)
>=3sqrt(2)