Properties sine and cosine of complex number and logarithmic function

Properties sine and cosine of complex number:
Properties of sine for complex number:
1-sin(z+2k?)=sinz
2-sin(z1+z2 )=sinz1cosz2+cosz1sinz2
3- sin(z1-z2 )=sinz1cosz2-cosz1sinz2
4- sin(z+? )=-sinz
5- sin(z+?/2 )=cosz
6- sinz 2=sin2x+sinh2y
7-sin(-z)=-sinz
8-sin(iz)=isinhz
9-d/dz sinz=cosz
Properties of cosine for complex number:
1-d/dz cosz=-sinz
2-cos(-z)=cosz
3-cos(z1+z2)=cosz1cosz2-sinz1sinz2
4-cos(z1-z2)= cosz1cosz2+sinz1sinz2
5-cos2z=1-sin2z
6-cos(z+?)=-cosz
7-cos2z=cos2z-sin2z
=2cos2z-1
hyperbolic function:
the hyperbolic sine ,cosine , tan and cot for complex number:
sinhz=(ez-e-z)/2
coshz=(ez+e-z)/2
tanhz=( ez-e-z)/( ez+e-z)
cotchz=( ez+e-z)/( ez-e-z)
1-cosh(iz)=cosz
2-sinh(-z)=-sinhz
3-cosh(-z)=coshz
4-Sinh(z1+z2)=sinhz1coshz2+coshz1sinhz2

=1-2sin2z
8-cosz1+cosz2=2cos(z1+z2)/2.cos(z1-z2)/2
9- cosz1-cosz2=-2sin(z1+z2)/2.sin(z1-z2)/2
10-cos(iz)=coshz
11-cosz=cosx coshy-isinx sinhy
12- cosz 2=cos2x+sinh2y
13-cosz=0 iff z=(2k+1)?/2 ,k?z
14- cosz = cosx
15-cosz=cosz
16-cos(iz)=cos(iz)