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What should be the influence of the imaginary part on a complex number?

I am asking because I am running a simulation model where the input is a complex number; say z=a+ib

Now the problem is that I get the same result when I put a=0 and give some high value to b, as when I do the vice-versa.

Should this behaviour be expected?

I look forward to a reply. Thank you in advance.

Regards,

Ila