Gnuplot and complex exponentials

Question

Could anyone tell me how to draw complex exponentials using gnuplot. I tried to draw them using this script, but argument `i` isn't recognized. ``` set terminal epslatex color colortext size 9cm,5cm set size 1.5,1.0 set output "eulerjeva_identiteta_1.tex" set style line 1 linetype 1 linewidth 3 linecolor rgb "#FF0055" set style line 2 linetype 2 linewidth 1 linecolor rgb "#FF0055" set style line 3 linetype 1 linewidth 3 linecolor rgb "#2C397D" set style line 4 linetype 2 linewidth 1 linecolor rgb "#2C397D" set style line 5 linetype 1 linewidth 3 linecolor rgb "#793715" set style line 6 linetype 2 linewidth 1 linecolor rgb "#793715" set style line 7 linetype 1 linewidth 3 linecolor rgb "#b1b1b1" set style line 8 linetype 3 linewidth 1 linecolor rgb "#b1b1b1" set grid set samples 7000 set key at graph .95, 0.4 set key samplen 2 set key spacing 0.8 f(x) = exp(i*x) g(x) = exp(-i*x) h(x) = exp(i*x)+exp(-i*x) set xrange [-2*pi:2*pi] set yrange [-1.2:1.2] set xtics ("$0$" 0, "$\pi$" pi, "$-…

Accepted Answer

Gnuplot doesn't understand `i` as `sqrt(-1)` because the variable `i` is not assigned a value by gnuplot--it is just another variable name as far as it is concerned. Gnuplot can understand and manipulate complex numbers using the format

```
z = {a,b}
```

which represents a complex number `z = (a + ib)` in written notation. So, i could be defined

```
i = {0.0,1.0}
```

There is still the problem of what you would get when you then graph

```
plot exp(i*x)
```

All the points are 'undefined' because they have an imaginary component. (Although, `h(x) = exp(i*x)+exp(-i*x)` would plot fine since it is purely real.) The problem is that gnuplot can plot only real quantities. You could try

```
plot real(exp(i*x)), imag(exp(i*x))
```

to visualize the components separately, or you could make a parametric plot:

```
set parametric
plot real(exp(i*t)), imag(exp(i*t))
```

Gnuplot and complex exponentials

Solution

Problem