What is factor e^{jw}+e^{-jw} ?

The solution to factor e^{jw}+e^{-jw} is e^{-jw}(e^{2jw}+1)

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factor e^{jw}+e^{-jw}

factor

e^{j w} + e^{- j w}

e^{- j w} (e^{2 j w} + 1)

Solution steps

e^{j w} + e^{- j w}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

= e^{- j w} e^{2 j w} + e^{- j w}

Factor out common term

e^{- j w}

= e^{- j w} (e^{2 j w} + 1)

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What is factor e^{jw}+e^{-jw} ?
The solution to factor e^{jw}+e^{-jw} is e^{-jw}(e^{2jw}+1)