What are the presentations of imaginary axis for different types of real coordinates?

[LearyJr]

Could you explain and depict geometrically imaginary axis for different types of real coordinates? I need it on order to understand their meanings both for physical applications IRL and further studying on pure mathematics.

 

[pka]

Could you explain and depict geometrically imaginary axis for different types of real coordinates? I need it on order to understand their meanings both for physical applications IRL and further studying on pure mathematics.

Your request is huge and vague. To do you justice it would take a chapter in a complex variables textbook such as this classic
You can find others in any good mathematics library,

 

[LearyJr]

Thank you for writing me back.
However, I've got several questions on your answer.
Firstly, what do you mean understand my huge request?
Secondly, why is it vague? I consider, there are no mistakes in my message.
To finish with, I haven't got any clear satisfactory answers.
Unfortunately, there is negative one.

 

[Dr.Peterson]

What do you mean by "different types of real coordinates"? Why would there be an imaginary axis at all for something that is real? And what sort of "depiction" or "presentation" are you thinking of?

Can you at least give a specific example?

 

[pka]

Firstly, what do you mean understand my huge request?

What don't you understand about the sentence: " To do you justice it would take a whole chapter in a complex variables textbook"?

 

[LearyJr]

I mean the Cartesian coordinates - both xy-plane coordinates and xyz-coordinates.
The problem is that I can't note the position of imaginary axis for xyz-coordinates.
All I understand is that the imaginary axis for xy-coordinates is arbitrarly perpendicular to Re x-axis and Re y-axis. All I need is to know the position of imaginary axis to Re x-, Re y- and Re x-axis. Thank you for your attention and understand.

 

[tkhunny]

All I need is to know the position of imaginary axis to Re x-, Re y- and Re x-axis.

Herein lies the problem with responding to your question.

1) "position" is not a useful concept in this context. Too much grounding in visualization. This will not get you far.
2) Feel free to read PKA's book on Complex Analysis and maybe pick up some Linear Algebra in order to gain a better understanding of a Basis of a Vector Space and the concept of Orthogonality.

 

[Deleted member 4993]

...To finish with, I haven't got any clear satisfactory answers. Unfortunately, there is negative one.

pka provided you with a reference book. Did you study that reference?