[tex]\text{Formula lui Euler:} \\ \\ e^{ix} = \cos x+i\sin x \\ \\ \\ \text{De exemplu:} \\\\ 2^i = e^{\ln(2^i)} = e^{i\ln 2} \,\,\Leftrightarrow\,\,2^i =\cos(\ln 2)+i\sin (\ln 2)\\ \\ \\ \text{Identitatea lui Euler:}\\ \\ e^{i\pi}+1 = 0 \,\, \Leftrightarrow\,\, e^{i\pi} = -1<0[/tex]
[tex]\\\text{Alta identitate:}\\ \\\ln(i) = i\,\dfrac{\pi}{2}\\ \\ i^i = e^{\ln i^i} = e^{i\ln i} = e^{i\cdot \frac{i\pi}{2}} = e^{-\frac{\pi}{2}}\,\, \Leftrightarrow\,\, i^i = e^{-\frac{\pi}{2}}[/tex]
