What is 1/2 e^{jθ}*1/2 e^{jθ} ?

The solution to 1/2 e^{jθ}*1/2 e^{jθ} is 1/4 e^{2jθ}

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simplify 1/2 e^{jθ}*1/2 e^{jθ}

simplify

\frac{1}{2} e^{j θ} \cdot \frac{1}{2} e^{j θ}

\frac{1}{4} e^{2 j θ}

Solution steps

\frac{1}{2} e^{j θ} \frac{1}{2} e^{j θ}

Apply exponent rule:

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

e^{j θ} e^{j θ} = e^{j θ + j θ}

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

Add similar elements:

j θ + j θ = 2 j θ

= \frac{1}{2} \cdot \frac{1}{2} e^{2 j θ}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2} e^{2 j θ}

\frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4}

= \frac{1}{4} e^{2 j θ}

e^{- \frac{2 k}{x}}

53 π \cdot 1 0^{- 6}

(e^{3 x^{2}})^{^{'}}

e^{- 3.7} \cdot 3. 7^{2}

(e^{3 t})^{3} \cdot \frac{s - 4}{s + 10}

What is 1/2 e^{jθ}*1/2 e^{jθ} ?
The solution to 1/2 e^{jθ}*1/2 e^{jθ} is 1/4 e^{2jθ}