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coercion code in Sage ?

Hi

why I have to add I in fz(z,zc)=uz+I*vz --> fz(z,zc,I)=uz+I*vz ?

to avoid error ?

var('x,y',domain='real')
var('z',domain='complex')
var('zc',domain='complex',latex_name=r'\overline{z}')

u(x,y)=x*y^2+y*x ;v(x,y)=x^2*y-y*x
fuv(x,y)=u(x,y)+I*v(x,y)

zDic={x:(z+zc)/2,y:(z-zc)/2}
uz(z,zc)=u.subs(zDic)
vz(z,zc)=v.subs(zDic)

show("uz : \t ", uz)
show("vz : \t ", vz)
fz(z,zc)=uz+vz
fz(z,zc)=uz+I*vz
#fz(z,zc,I)=uz+I*vz