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- Real function z = f(x,y) in the real space :

- Real function z = f(x) on the real axis x is cross-section in above figure on y-axis when y=0 :

- Complex function re(z) = re(f(x,y)), Real part of complex value in the real space :

- Complex function z = re(z) + im(z) i, re(z) = re(f(x)) and im(z) = im(f(x)), Real (blue) + imaginary (red) part on the real axis x is cross-section in above figure on y-axis when y=0 :

- re(z) = re(f(complex(x,y))), Real part of complex value in the complex plane :

- re(z(x)) = re(f(complex(x,yy))), yy is parameter as y, 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.

- re(z(x)) = re(f(complex(xx,x))), xx is parameter as x, Real part of complex value on the imaginary axis y is cross-section on x axis:

- im(z) = im(f(x,y)), Imaginary part of complex value in the real space :

- im(z(x)) = im(f(x)), Imaginary part of complex value on the real axis x is cross-section in above figure on y-axis when y=0 :

- im(z) = im(f(complex(x,y))), Imaginary part of complex value on the complex plane:

- im(z(x)) = im(f(complex(x,yy))), yy is parameter as y, 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.

- im(z(x)) = im(f(complex(xx,x))), xx is parameter as x, Imaginary part of complex value on the imaginary axis y is cross-section on x axis:

- z = figure 6 + figure 10 = re(z)+ im(z) 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:

- z = figure 7 + figure 12 = re(z) + im(z) i = Real (blue) + imaginary (red) part of complex value on the imaginary axis y is cross-section on x axis:

- abs(z) = abs(f(complex(x,y))), Absolute value of complex value on the complex plane:

## Reference

Function category: complex functions
Function category: complex math