Evaulate $\cosh(1-i\sqrt{3})$ Going through some exercises in complex functions and I get $\frac{1}{2}(ee^{-i\sqrt{3}} + e^{-1}e^{i\sqrt{3}})$ but not sure if I can simplify this further?
Thanks

Notice, $$\cosh(1-i\sqrt 3)=\frac{e^{1-i\sqrt 3}+e^{-1+i\sqrt 3}}{2}$$
$$=\frac{ee^{-i\sqrt 3}+e^{-1}e^{i\sqrt 3}}{2}$$
$$=\frac{e(\cos(\sqrt 3))-i\sin(\sqrt 3))+e^{-1}(\cos(\sqrt 3)+i\sin(\sqrt 3))}{2}$$
$$=\frac{(e+e^{-1})\cos(\sqrt 3)-i(e-e^{-1})\sin(\sqrt 3)}{2}$$
$$=\left(\frac{e+e^{-1}}{2}\right)\cos(\sqrt 3)-i\left(\frac{e-e^{-1}}{2}\right)\sin(\sqrt 3)$$
$$=\cosh (1)\cos(\sqrt 3)-i\sinh (1)\sin(\sqrt 3)$$
