simplificar 1/2 e^{jθ}*1/2 e^{jθ}

Solução

simplificar

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

\frac{1}{4} e^{2 j θ}

Passos da solução

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

Aplicar as propriedades dos expoentes:

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}

Somar elementos similares:

j θ + j θ = 2 j θ

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

Multiplicar frações:

\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}

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