$\mathit{\text{Euler's Identity}}$

$e^{jx}=cos\left(x\right)+jsin\left(x\right)$

$e^{-jx}=cos\left(x\right)-jsin\left(x\right)$

$\mathit{\text{Sine in complex exponentials}}$

$\boxed{sin\left(x\right)=\frac{e^{jx}-e^{-jx}}{2j}}$

$\mathit{\text{Cosine in complex exponentials}}$

$\boxed{cos\left(x\right)=\frac{e^{jx}+e^{-jx}}{2}}$

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