Euler's identity

ejθ=cos(θ)+jsin(θ)e−jθ=cos(θ)−jsin(θ)cos(θ)=12(ejθ+e−jθ)sin(θ)=12j(ejθ−e−jθ)\begin{align} e^{j\theta} = \cos(\theta) + j \sin(\theta)\\ e^{-j\theta} = \cos(\theta) - j \sin(\theta) \\ \\ \cos(\theta)=\frac{1}{2}(e^{j\theta}+e^{-j\theta})\\ \sin(\theta)=\frac{1}{2j}(e^{j\theta}-e^{-j\theta}) \end{align}

References

  1. review of basic math for signals and systems by Henry D. Pfister: http://pfister.ee.duke.edu/courses/ece485/math_review.pdf
  2. https://en.wikipedia.org/wiki/Euler's_identity