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.