sin(z)=2i1(eiz−e−iz)=2i1(ei(x+iy)−e−i(x+iy))=2i1(eixe−y−e−ixey)=2i1[(cos(x)+isin(x))e−y−(cos(x)−isin(x))ey]=2i1[cos(x)(e−y−ey)+isin(x)(e−y+ey)]=2icos(x)(ey−e−y)+21sin(x)(ey+e−y)=icos(x)sinh(y)+sin(x)cosh(y)=2sin(x)cosh(y)=2cos(x)sinh(y)=0x=2π+kπ,k∈Zkgerade : cosh(y)=2y=±arcosh(2)kungerade : −cosh(y)=2keineLo¨sungz=x+iy=2π+2nπ±iarcosh(2),n∈Z