# Euler's Formula **The fundamental relationship between the [[trigonometric functions]] and the [[Exponential Function#Complex exponential function|complex exponential function]].** > [!NOTE] Euler's Formula > *Euler's formula* states that for any real number $x$ > $e^{i\theta}=\cos \theta+i\sin \theta$ > - $e$ - [[e|Euler's number]] > - $i$ - the [[Complex Number|imaginary unit]] Euler's formula is used to derive [[De Moivre's Formula|de Moivre's formula]].