Đẳng thức lũy thừa số phức

$\sin \theta =\mathrm {Re} (e^{i\theta })={\frac {e^{i\theta }-e^{-i\theta }}{2i}}$

$\cos \theta =\mathrm {Im} (e^{i\theta })={\frac {e^{i\theta }+e^{-i\theta }}{2}}$

$\tan \theta ={\frac {\sin \theta }{\cos \theta }}={\frac {e^{2i\theta }-1}{i(e^{2i\theta }+1)}}$

$\csc \theta ={\frac {1}{\sin \theta }}={\frac {2i}{e^{i\theta }-e^{-i\theta }}}$

$\sec \theta ={\frac {1}{\cos \theta }}={\frac {2}{e^{i\theta }+e^{-i\theta }}}$

$\cot \theta ={\frac {1}{\tan \theta }}={\frac {i(e^{2i\theta }+1)}{e^{2i\theta }-1}}$