What is expand (e^{jθ}-e^{-jθ})^2 ?

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

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expand (e^{jθ}-e^{-jθ})^2

expand

(e^{j θ} - e^{- j θ})^{2}

e^{2 j θ} - 2 + e^{- 2 j θ}

Solution steps

(e^{j θ} - e^{- j θ})^{2}

Apply Perfect Square Formula:

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

a = e^{j θ}, b = e^{- j θ}

= (e^{j θ})^{2} - 2 e^{j θ} e^{- j θ} + (e^{- j θ})^{2}

Simplify

(e^{j θ})^{2} - 2 e^{j θ} e^{- j θ} + (e^{- j θ})^{2} : e^{2 j θ} - 2 + e^{- 2 j θ}

= e^{2 j θ} - 2 + e^{- 2 j θ}

(2) (x ln (x) - x)

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