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simplificar 1/2 (2(-2)+4(1/2))^{-1/2}

Solución

simplificar

\frac{1}{2} (2 \cdot (- 2) + 4 \cdot (\frac{1}{2}))^{- \frac{1}{2}}

- \frac{1}{2 \cdot 2 ^{\frac{1}{2}}} i

Pasos de solución

\frac{1}{2} (2 (- 2) + 4 (\frac{1}{2}))^{- \frac{1}{2}}

Aplicar la propiedad:

(a) = a

(\frac{1}{2}) = \frac{1}{2}

= \frac{1}{2} (2 (- 2) + 4 \cdot \frac{1}{2})^{- \frac{1}{2}}

Aplicar las leyes de los exponentes:

a^{- b} = \frac{1}{a ^{b}}

(2 (- 2) + 4 \cdot \frac{1}{2})^{- \frac{1}{2}} = \frac{1}{( 2 ( - 2 ) + 4 \cdot \frac{1}{2} ) ^{\frac{1}{2}}}

= \frac{1}{2} \cdot \frac{1}{( 2 ( - 2 ) + 4 \cdot \frac{1}{2} ) ^{\frac{1}{2}}}

(2 (- 2) + 4 \cdot \frac{1}{2})^{\frac{1}{2}} = 2^{\frac{1}{2}} i

= \frac{1}{2} \cdot \frac{1}{2 ^{\frac{1}{2}} i}

Multiplicar por el conjugado

\frac{- i}{- i}

= \frac{1}{2} \cdot \frac{1 \cdot ( - i )}{2 ^{\frac{1}{2}} i ( - i )}

Simplificar

\frac{1 \cdot ( - i )}{2 ^{\frac{1}{2}} i ( - i )} : \frac{- i}{2 ^{\frac{1}{2}}}

= \frac{1}{2} \cdot \frac{- i}{2 ^{\frac{1}{2}}}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

\frac{- i}{2 ^{\frac{1}{2}}} = - \frac{i}{2 ^{\frac{1}{2}}}

= \frac{1}{2} (- \frac{i}{2 ^{\frac{1}{2}}})

Aplicar la propiedad:

a (- b) = - ab

\frac{1}{2} (- \frac{i}{2 ^{\frac{1}{2}}}) = - \frac{1}{2} \cdot \frac{i}{2 ^{\frac{1}{2}}}

= - \frac{1}{2} \cdot \frac{i}{2 ^{\frac{1}{2}}}

Aplicar las propiedades de las fracciones:

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

= - \frac{1 i}{2 \cdot 2 ^{\frac{1}{2}}}

Aplicar la propiedad:

1 \cdot a = a

1 i = i

= - \frac{i}{2 \cdot 2 ^{\frac{1}{2}}}

Rewrite in standard complex form:

- \frac{1}{2 \cdot 2 ^{\frac{1}{2}}} i

= - \frac{1}{2 \cdot 2 ^{\frac{1}{2}}} i

2 e^{- 9 \cdot 2}

- \frac{3}{5}

4 3 j

729

\frac{4}{9} \frac{25}{16}