What is expand (e^{(jω)/2}-e^{-(jω)/2})^2 ?

The solution to expand (e^{(jω)/2}-e^{-(jω)/2})^2 is e^{jω}-2+e^{-jω}

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expand (e^{(jω)/2}-e^{-(jω)/2})^2

expand

(e^{\frac{jω}{2}} - e^{- \frac{jω}{2}})^{2}

e^{jω} - 2 + e^{- jω}

Solution steps

(e^{\frac{jω}{2}} - e^{- \frac{jω}{2}})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = e^{\frac{jω}{2}}, b = e^{- \frac{jω}{2}}

= (e^{\frac{jω}{2}})^{2} - 2 e^{\frac{jω}{2}} e^{- \frac{jω}{2}} + (e^{- \frac{jω}{2}})^{2}

Simplify

(e^{\frac{jω}{2}})^{2} - 2 e^{\frac{jω}{2}} e^{- \frac{jω}{2}} + (e^{- \frac{jω}{2}})^{2} : e^{jω} - 2 + e^{- jω}

= e^{jω} - 2 + e^{- jω}

cos (x^{2} + 3 y - 1) (2 x + 3 \frac{d y}{d x})

\frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) \cdot ( s - 3 ) \cdot ( s + 1 ) ^{2}}

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\frac{1}{( s + 2 ) ( s + 3 )}

What is expand (e^{(jω)/2}-e^{-(jω)/2})^2 ?
The solution to expand (e^{(jω)/2}-e^{-(jω)/2})^2 is e^{jω}-2+e^{-jω}