${\displaystyle {}z=x+{\mathrm {i} }y}$

${\displaystyle {}\exp z=(\exp x)(\cos y+{\mathrm {i} }\sin y)\,.}$

${\displaystyle {}\cos z={\frac {\exp \left({\mathrm {i} }z\right)+\exp \left(-{\mathrm {i} }z\right)}{2}}\,}$

und

${\displaystyle {}\sin z={\frac {\exp \left({\mathrm {i} }z\right)-\exp \left(-{\mathrm {i} }z\right)}{2{\mathrm {i} }}}\,.}$

${\displaystyle {}\cos(z+w)=\cos z\,\cos w-\sin z\,\sin w\,}$

und

${\displaystyle {}\sin(z+w)=\sin z\,\cos w+\cos z\,\sin w\,.}$

${\displaystyle {}(\cos z)^{2}+(\sin z)^{2}=1\,.}$