If you mean by "practically" the way we represent during hard implementation, you can represent the real and imaginary parts independently and do operations without explicitly represented in complex form.

If I am interpreting your question correctly then you basically are asking about representation from hardware point of view,if that's the case then you can use separate memory segments for real and complex parts.Complex representation is for mathematical analysis on hardware level it just numbers stored in binary form in segments of memory.So you can separately store the real and complex part in memory segments and design retrieval algorithm accordingly.

You can use the matrix representation of a complex number

for implementation:

a+jb eqvt matrix see below

a+jb == [ a -b ; b a]

Then use matrix operations .

Cheers

Dears Mr. Mustapha Djeddou and Mr. Sanskar Singh thank you for your responses.

Dear Mr. Narasim Ramesh

I did read about this solution, but do you think that this way maybe increase the bandwidth required? (repetition the elements in the matrix!)

@ Hind Thanoon

I am not sure I understand "Bandwidth" in this context

but if you mean memory and computation , some clever

implementation may be possible .

Cheers

Dear Hind,

In digital communication system one is faced in complex number representations in base band modulation, where one maps the digital binary numbers on the modulation constellation symbols which are complex values.

On representation is to represent them in an I sequence and a Q sequence such that z= i+j Q. So, practically, the complex numbers are represented by two branches,the I branch and the Q branch. In order not to consume bandwidth one use the sine and cosine carriers at the end of the channels.

You can represent them also as an order pair x,y in case of mathematical operation on them. In case of multiplication you change then into polar form mag. z and angle of z.

Best wishes

Dear Mr. Abdelhalim abdelnaby Zekry

Thank you for your response, I thought there was a problem when I use a complex number in the baseband system.