Can you answer this problem, cosh (-x + iy)

cosh(t) = (1/2) * (e^(t) + e^(-t))

cosh(-x + iy) =
(1/2) * e^(-x + iy) + e^(-(-x + iy)) =
(1/2) * (e^(iy - x) + e^(x - iy) =
(1/2) * (e^(iy) / e^(x) + e^(x) / e^(iy)) =
(1/2) * ((cos(y) + i * sin(y)) / e^(x) + e^(x) / (cos(y) + i * sin(y))) =
(1/2) * ((cos(y) + i * sin(y))^2 + e^(2x)) / (e^(x) * (cos(y) + i * sin(y))) =
(1/2) * (cos(y)^2 + 2 * sin(y) * cos(y) * i - sin(y)^2 + e^(2x)) / (e^(x) * (cos(y) + i * sin(y))) =
(1/2) * (cos(2y) + i * sin(2y) + e^(2x)) / (e^(x) * (cos(y) + i * sin(y))) =>
(1/2) * (cos(2y) + i * sin(2y) + e^(2x)) * (cos(y) - i * sin(y)) / (e^(x) * (cos(y)^2 + sin(y)^2)) =
(cos(2y) + i * sin(2y) + e^(2x)) * (cos(y) - i * sin(y)) / e^(x) =
(e^(2y * i) + e^(2x)) / e^(x) =
e^(2y * i - x) + e^(x)