Auteur: Serge Boisse
Date: Le 26/03/2023 à 16:03
Type: web/MOC
Tags: 
pub: oui
commentaires: ouiCopier

Image of a point by a complex function: the online application!

This interactive application allows you to visually see the image of a point or a straight line by any function in the complex plane.

Enter a function f(z) such as e^z, and move the red dot. The yellow point will be the image in the complex plane of z. Moreover, as a bonus, this interactive application gives the image by f of a cross centered on the cursor! Click in the white field below to enter any function of the variable z and move the red dot!

Syntaxe à utiliser pour entrer la fonction z->f(z)

Some examples z^2
zz*
(z+1)/(z-1)
sin(z)
e^z
log(z)
sech(z)
arctan(z)
z^3-1
0.926(z+7.3857e-2 z^5+4.5458e-3 z^9)
Jacobi elliptic sn(z, 0.3)
Gamma function gamma(z)
Iterated function iter(z+z*^2,z,12)

Les constantes i, pi et e are recognized and multiplication is implicit ; so e^iz is equivalent to exp(i*z).
z* is the complex conjugate of z, so zz* is the square root of the modulus. But you can get the modulus itself whith  |z| ou si vous préférez, modulus(z).
* is multiplication ^ the power operator. but for compatibility with programming langages, ** is also the power operator? Be careful as z**2 reads like 'z^2'.
If you want to multiply the conjugate of z by 2, use (z*)*2 or  2*z*.
Finally, z! is the factorial of z and it works even if z is complex, thanks obviously to the gamma function.
The recognized functions are ::

• random(): Gives a complex random number of module between 0 and 1.
• re(z), im(z) :real and imaginary parts.
• modulus(z), argz()
• floor(z), ceil(z)
• square(z), cube(z), sqrt(z)
• exp(z) = e^z, log(z)
• sin(z), cos(z), tan(z), cot(z), sec(z), csc(z)
• asin(z), acos(z), atan(z). names like arcsin...are also valid:
• arcsin, arccos, arctan, arccot, arcsec, arccsc
• sinh(z), cosh(z), tanh(z), coth(z), sech(z), csch(z) :complex hyperbolic trig !
• arcsinh(z), arccosh(z), arctanh(z), arccoth(z), arcsech(z), arccsch(z)
• gamma(z)
• pow(a,b) équivalent de a^b ou a**b
• binomial(a,b)
• sn(z,k), cn(z,k), dn(z,k) : Jacobi elliptic functions
• sum(f(z,n),N) : returns the sum of the values f(z,n) for n varying from 0 to N-1. For example sum(z**-n,5)
• iter(f(z),z,n) : will iterate f acting on z, n times.