how can one say whether a+ib is greater or c+id is greater ?"i" has its usual meaning, i.e. "iota"

Two complex numbers cannot be compared. We can compare its
absolute values, because they are real numbers, but there is not an order relation
between two complex number because the complex number field is not
ordered.

All we can say about two complex numbers is if
they are equal or not. We can do this by comparing the real parts and imaginary
parts.

For instance, the given complex numbers z1 = a+bi
and z2=c+di are equal if a=c and b=d. If not, z1`!=` z2, but we cannot say if
z1>z2 or z1<z2.

Since a complex number can be
viewed as a position vector, you can also say how far from origin a point is. But for
this reason, we'll have to calculate the distance from origin to that point and this
represents the absolute value of the complex number.