What is expand (1+e^{-jx})(1+e^{+jx}) ?

The solution to expand (1+e^{-jx})(1+e^{+jx}) is e^{-jx}+e^{jx}+2

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expand (1+e^{-jx})(1+e^{+jx})

expand

(1 + e^{- j x}) (1 + e^{+ j x})

e^{- j x} + e^{j x} + 2

Solution steps

(1 + e^{- j x}) (1 + e^{j x})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = e^{- j x}, c = 1, d = e^{j x}

= 1 \cdot 1 + 1 \cdot e^{j x} + e^{- j x} \cdot 1 + e^{- j x} e^{j x}

= 1 \cdot 1 + 1 \cdot e^{j x} + 1 \cdot e^{- j x} + e^{- j x} e^{j x}

Simplify

1 \cdot 1 + 1 \cdot e^{j x} + 1 \cdot e^{- j x} + e^{- j x} e^{j x} : e^{- j x} + e^{j x} + 2

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

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(x - h)^{2} + (y - k)^{2} + (z - l)^{2^{^{'}}}

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