# How to compute itEdit

One can use Maxima CAS to find it :

(%i1) z: x+y*%i;
(%o1) %i*y+x
(%o2) %i*y+x
(%i3) realpart(sinh(z));
(%o3) sinh(x)*cos(y)
(%i8) trigrat(sinh(x));
(%o8) (%e^−x*(%e^(2*x)−1))/2
(%i11) expand(%);
(%o11) %e^x/2−%e^−x/2


sin(Z) =

$Real = \sin(x) ((\exp(y) + \exp(-y))/2)$

$Imag = \cos(x) ((\exp(y) - \exp(-y))/2)$

cos(Z)

$Real = \cos(x) ((\exp(y) + \exp(-y))/2)$

$Imag = -\sin(x) ((\exp(y) - \exp(-y))/2)$

sinh(Z)

$Real = \cos(y) ((\exp(x) - \exp(-x))/2)$

$Imag = \sin(y) ((\exp(x) + \exp(-x))/2)$

cosh(Z)

$Real = \cos(y) ((\exp(x) + \exp(-x))/2)$

$Imag = \sin(y) ((\exp(x) - \exp(-x))/2)$

# ImagesEdit

This image shows the Julia set of acomplex function of the form f(z)=a*sin(z), where a is a suitably chosen number in the interval (0,1).