1. Space curve in the real space (x,y,f) :
2. Surface of Real function f(x,y) in the real space (x,y,f)
3. Real function f(x) on the real axis x
4. Surface of Complex function re(f) = re(f(x,y)), Real part of complex value in the real space (x,y,re(f)) :
5. Complex function re(f) + im(f), on the real axis x
6. Derivative of Complex function re(f) + im(f), on the real axis x
7. Second order derivative of Complex function re(f) + im(f), on the real axis x
8. Half order derivative of Complex function re(f) + im(f), on the real axis x
9. Integral of Complex function re(f) + im(f), on the real axis x
10. Real part of complex value in the complex plane
11. Real part of complex value on the real axis x
12. Real part of complex value on the imaginary axis y
13. Imaginary part of complex value in the real plane (x,y)
14. Imaginary part of complex value on the real axis x
15. Imaginary part of complex value on the complex plane
16. Imaginary part of complex value on the real axis x
17. Imaginary part of complex value on the imaginary axis y
18. complex value on the real axis x
19. complex value on the imaginary axis y
20. Absolute value of complex value on the complex plane

1. Space curve in the real space (x,y,f) :
2. Surface of Real function f(x,y) in the real space (x,y,f) :
3. Real function f(x) on the real axis x is cross-section in above figure on y-axis at y=0 :
4. Surface of Complex function re(f) = re(f(x,y)), Real part of complex value in the real space (x,y,re(f)) :
5. Complex function f(z) = re(f) + im(f), re(f) = re(f(x)) and im(f) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is cross-section in above figure on y-axis at y=0 :
6. Derivative of Complex function f(z) = re(f) + im(f), re(f) = re(f(x)) and im(f) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is derivative in above figure on y-axis at y=0 :
7. Second order Derivative of Complex function f(z) = re(f) + im(f), re(f) = re(f(x)) and im(f) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is Second order Derivative in above figure on y-axis at y=0 :
8. Half order Derivative of Complex function f(z) = re(f) + im(f), re(f) = re(f(x)) and im(f) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is Half order Derivative in above figure on y-axis at y=0 :
9. Integral of Complex function f(z) = re(f) + im(f), re(f) = re(f(x)) and im(f) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is Integral in above figure on y-axis at y=0 :
10. re(f) = re(f(complex(x,y))), Real part of complex value in the complex plane :
11. re(f) = re(f(complex(x,y))), x is independent variable and y is parameter, Real part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 4 when y=0.
12. re(f) = re(f(complex(x,y))), x is parameter and y is independent variable, Real part of complex value on the imaginary axis y is cross-section on x axis:
13. im(f) = im(f(x,y)), Imaginary part of complex value in the real plane (x,y) :
14. im(f) = im(f(x)), Imaginary part of complex value on the real axis x is cross-section in above figure on y-axis at y=0 :
15. im(f) = im(f(complex(x,y))), Imaginary part of complex value on the complex plane:
16. im(f) = im(f(complex(x,y))), x is independent variable and y is parameter, Imaginary part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 9 when y=0.
17. im(f) = im(f(complex(x,y))), x is parameter and y is independent variable, Imaginary part of complex value on the imaginary axis y is cross-section on x axis:
18. f = figure 6 + figure 10 = re(f)+ im(f) i = Real (blue) + imaginary (red) part of complex value on the real axis x is cross-section on y axis in above figure. It is the same as Figure 4 when y=0:
19. f = figure 7 + figure 12 = re(f) + im(f) i = Real (blue) + imaginary (red) part of complex value on the imaginary axis y is cross-section on x axis:
20. abs(f) = abs(f(complex(x,y))), Absolute value of complex value on the complex plane:

Reference