@Markiyan Hirnyk Well, it depends on how you would like the complex numbers to be represented in Excel. What I did before was only exporting Real and Imaginary parts as numbers and the whole complex numbers as a text (or string)!
Thanks to your comment I looked more into it and found out that Excel has a constructor for complex numbers and several functions for computing with complex numbers (at least MS Excel 2007). So another possibility can be:
A := LinearAlgebra[RandomMatrix](2, 4, generator = rand(0 .. 5)+I*rand(-3 .. 5));
complex_numbers := map(x -> cat("=Complex(", Re(x), ";", Im(x), ")"), A);
Export(complex_numbers, "D:/example2.xls", "Complex numbers", "A2");
Which results in this Excel file:
Now, there are really complex numbers (how Excel takes it), but it should be evaluated. I can evaluate only cell after cell (which is so impractical) to get:
Excel (at least the 2007 version) can perform some computations with those numbers, but it is nothing "great". When I try e.g. "=IMPOWER("i";2)", which should be equal to -1 (=i^2), I get: