# x

1. Real function z = f(x,y) in the real space :
2. Real function z = f(x) on the real axis x is cross-section in above figure on y-axis when y=0 :
3. Complex function re(z) = re(f(x,y)), Real part of complex value in the real space :
4. 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 :
5. re(z) = re(f(complex(x,y))), Real part of complex value in the complex plane :
6. 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.
7. 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:
8. im(z) = im(f(x,y)), Imaginary part of complex value in the real space :
9. 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 :
10. im(z) = im(f(complex(x,y))), Imaginary part of complex value on the complex plane:
11. 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.
12. 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:
13. 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:
14. 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:
15. 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