>>45
(a+bi)/c is a ratio of complex-to-real. real-to-real is okay. complex-to-real takes from two different fields. A field only has closure for an operation if you can get back to the same field through the operation. as complex and real are different fields, division isn't necessarily closed, mirite?
that's why (a+bi)/c is incorrect and a/c+i*b/c is correct. the latter only has real-to-real ratios (one of them being multiplied by i), while the former has a complex over real which, like i said, takes from two different fields.