inverseW(x)

Content
  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
A complex function is a function from complex numbers to complex numbers, its domain is complex z=complex(x,y).
  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

  • Function category: complex functions
  • Function category: complex math

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