e^(-2 $\pi$ jf)-e^(2 $\pi$ jf)

asked by guest
on Nov 11, 2024 at 2:33 pm



You asked:

Evaluate the expression: \({e}^{-\left( 2 \cdot \pi \cdot j f \right)} - {e}^{2 \cdot \pi \cdot j f}\)

MathBot Answer:

Evaluated



\(\displaystyle {e}^{-\left( 2 \cdot \pi \cdot j f \right)} - {e}^{2 \cdot \pi \cdot j f} = - e^{2 f j \pi} + e^{- 2 f j \pi} \)

Factored

\[{e}^{-\left( 2 \cdot \pi \cdot j f \right)} - {e}^{2 \cdot \pi \cdot j f} = - \left(e^{f j \pi} - 1\right) \left(e^{f j \pi} + 1\right) \left(e^{2 f j \pi} + 1\right) e^{- 2 f j \pi}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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