﻿ AI math handbook calculator - Fractional Calculus Computer Algebra System software
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## Complex Function plot

With this tool you can visualize complex-valued functions
by assigning a color to each point in the complex plane
according to its argument/phase.
The identity function f(z)=z shows how colors are assigned.

Input box:
Enter any expression in z. Here are some example functions to try:

• z
• arctan(z)
• re(arctan(z)) real part
• im(arctan(z)) imag part
• arctan(z-random())
• z^4-1
• (z^2-i)/(i*z-1)^2
• sin(z)-e^(cos(z))
• log(z)-sech(z-i)
• (z-1)(conj(z)^2-conj(z)-1)
• 0.926(z-7.3857e-2*z^5-4.5458e-3*z^9)
• special function: gamma(z), zeta(z)
• Jacobi Elliptic: sn(z,0.3), cn(z,0.3), dn(z,0.3)
• Taylor Series: cos(z)=sum((-1)^n*z^(2n)/(2n)!,7) parameter must be n
• Atomic Singular Inner Function: prod(e^((z*(e^(2*pi*i/5))^n)/(z-(e^(2*pi*i/5))^n)),5) parameter must be n
• Iterated function: iter(z-z'^2,z,15)

Parameters: You can also use three parameters t,n,u in your function, e. g.

• t, where 0 ≤ t ≤ 1,
• u, where u = exp(i*s) and 0 ≤ s ≤ 2pi
• n, with 0 ≤ n ≤ 30

Zoom In/Out:
Press button (+) to zoom in or (-) to zoom out. Alternatively use the mouse wheel. You can also change the view by dragging the plot.

Its independent variable must be z. put mouse on the graph to show
Mouse z: (re,im) on upper left and values of f(z): (re,im) on upper right.

• random(), re(z), im(z), modulus(z), arg(z), recip(z), neg(z), conj(z), disk(z), floor(z), ceil(z), square(z), cube(z), sqrt(z), exp(z), log(z),
• trig function :
sin(z), cos(z), tan(z), cot(z), sec(z), csc(z), sinh(z), cosh(z), tanh(z), coth(z), sech(z), csch(z),
• inverse trig function :
asin(z), acos(z), atan(z), acot(z), asec(z), acsc(z), asinh(z), acosh(z), atanh(z), acoth(z), asech(z), acsch(z), arcsin(z), arccos(z), arctan(z), arccot(z), arcsec(z), arccsc(z), arcsinh(z), arccosh(z), arctanh(z), arccoth(z), arcsech(z), arccsch(z),
• special function :
gamma(z), pow(z, 2), rationalBlaschke(z, 2), mobius(z, 2, 3, 4, 5), psymbol(z, 2), binet(z), joukowsky(z, 2, 3), zeta(z), dirichletEta(z), binomial(z, 2), sn(z, 0.2), cn(z, 0.2), dn(z, 0.2), sum(z, 2), prod(z, 2), blaschke(z, 2), iter(z, z, 3),

## Complex

1. complex - complex function - complex math
2. complex animate(z) for phase animation, the independent variable must be z.
3. complex plot(z) for phase and/or modulus, the independent variable must be z.
4. complex2D(x) for complex 2 curves of real and imag parts, the independent variable must be x.
5. complex3D(x) for 3 dimensional graph, the independent variable must be x.
6. color WebXR surface of complex function on complex plane
7. Riemann surface - Complex Branches - complex coloring

## References

1. math handbook content 2 chapter 10 complex function
2. math handbook content 3 chapter 10 complex function
3. math handbook content 4 chapter 10 complex function
4. Complex analysis
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