Complex constants are expressed as {<real>,<imag>}, where <real> and <imag> must be numerical constants. For example, {3,2} represents 3 + 2i; {0,1} represents 'i' itself. The curly braces are explicitly required here.
Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and C. Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1", 3.5e-1, etc. The most important difference between the two forms is in division: division of integers truncates: 5/2 = 2; division of reals does not: 5.0/2.0 = 2.5. In mixed expressions, integers are "promoted" to reals before evaluation: 5/2e0 = 2.5. The result of division of a negative integer by a positive one may vary among compilers. Try a test like "print -5/2" to determine if your system chooses -2 or -3 as the answer.
The integer expression "1/0" may be used to generate an "undefined" flag, which causes a point to ignored; the ternary operator gives an example.
The real and imaginary parts of complex expressions are always real, whatever
the form in which they are entered: in {3,2} the "3" and "2" are reals, not
integers.