What is factor 2e^{-jθ^2}+2e^{jθ^2} ?

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

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factor 2e^{-jθ^2}+2e^{jθ^2}

factor

2 e^{- j θ^{2}} + 2 e^{j θ^{2}}

2 e^{- j θ^{2}} (1 + e^{2 j θ^{2}})

Solution steps

2 e^{- j θ^{2}} + 2 e^{j θ^{2}}

Apply exponent rule:

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

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

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

Rewrite as

= 1 \cdot 2 e^{- θ^{2} j} + 2 e^{- θ^{2} j} e^{2 θ^{2} j}

Factor out common term

2 e^{- θ^{2} j}

= 2 e^{- θ^{2} j} (1 + e^{2 θ^{2} j})

(x)^{6}

6 cos^{2} (x) + 5 cos (x) - 6

- (10)

2 a x + 6 a y - 3 b x - 9 b y

a^{s - 2} + a^{b - 1}

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