Treat them as vectors ... easy peasy ...
I've never heard that. What part is imaginary?
Using the complex form
a + bi gives us a unit vector approach ...
a times the real unit vector plus
b times the imaginary unit vector ... then add and multiply as usual ... with both closure and unique identities we can form our one-to-one correspondence and map our complex values straight into this vector form ... or any vector form for that matter ... pick whichever one is easiest to compute with ...
I've never had to deal with these values ... my understanding is that they crop up in electronics here and there ... [shrugs shoulders] ... I'm an uneducated construction laborer, what do you expect of me? ...
ETA: Scalar multiplication, my bad ...