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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.

    function :

  • 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),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),
  • inverse trig function :
    asin(z)=arcsin(z),acos(z)=arccos(z),atan(z)=arctan(z),acot(z)=arccot(z),asec(z)=arcsec(z),acsc(z)=arccsc(z),asinh(z)=arcsinh(z),acosh(z)=arccosh(z),atanh(z)=arctanh(z),acoth(z)=arccoth(z),asech(z)=arcsech(z),acsch(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),

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