#Plotting a Complex Function in GNUplot
set terminal png size 400, 300
set output 'complex_function.png'

# Set the title and labels
set title "Complex Function: f(x) = e^(ix)"
set xlabel "X-axis"
set ylabel "Y-axis"
set grid

# Define a complex function f(x) = e^(ix)
f_real(x) = cos(x)     # Real part: cos(x)
f_imag(x) = sin(x)     # Imaginary part: sin(x)
f_magnitude(x) = sqrt(f_real(x)**2 + f_imag(x)**2)  # Magnitude: |e^(ix)|
f_phase(x) = atan2(f_imag(x), f_real(x))            # Phase: arg(e^(ix))

# Plot the real part, imaginary part, magnitude, and phase of the complex function
plot f_real(x) with lines lw 2 title 'Re:cos(x)', \
     f_imag(x) with lines lw 2 title 'Im:sin(x)', \
     f_magnitude(x) with lines lw 2 title 'Magnitude', \
     f_phase(x) with lines lw 2 title 'Phase'