What is (e^{-jw})/(e^{j w/2)} ?

The solution to (e^{-jw})/(e^{j w/2)} is e^{-(3jw)/2}

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simplify (e^{-jw})/(e^{j w/2)}

simplify

\frac{e ^{- j w}}{e ^{j \frac{w}{2}}}

e^{- \frac{3 j w}{2}}

Solution steps

\frac{e ^{- j w}}{e ^{j \frac{w}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

= e^{- j w - j \frac{w}{2}}

Multiply

j \frac{w}{2} : \frac{j w}{2}

= e^{- j w - \frac{j w}{2}}

Join

- j w - \frac{w j}{2} : - \frac{3 j w}{2}

= e^{- \frac{3 j w}{2}}

e^{- 4.3}

e^{- j \cdot \frac{π}{3} \cdot 1 \cdot 1}

8. 1^{- 3} \cdot 1000

\frac{d}{d x} (e^{x + 2 y})

What is (e^{-jw})/(e^{j w/2)} ?
The solution to (e^{-jw})/(e^{j w/2)} is e^{-(3jw)/2}