Salut,
En suçant de son pouce que z = x + i.y
cos(z) = (e^(iz) + e^(-iz))/2
cos(z) = (e^(i.(x+iy) + e^(i.(-x-iy))/2
cos(z) = (e^(-y+ix) + e^(y-ix)/2
cos(z) = (1/2) * [e^-y * e^(ix) + e^y * e^(-ix)]
cos(z) = (1/2) * [e^-y * (cos(x)+i.sin(x)) + e^y * (cos(-x)+i.sin(-x))]
cos(z) = cos(x) * (e^-y + e^y)/2 + i.sin(x) * (e^-y - e^y)/2
cos(z) = cos(x) * ch(y) - i.sin(x) * sh(y)
|cos(z)|² = cos²(x) * ch²(y) + sin²(x) * sh²(y)
|cos(z)|² = cos²(x) * ch²(y) + (1 - cos²(x)) * sh²(y)
|cos(z)|² = cos²(x) * (ch²(y) - sh²(y)) + sh²(y)
|cos(z)|² = cos²(x) + sh²(y)