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受欢迎的代数 >

化简 1/2 (2(-2)+4(1/2))^{-1/2}

解答

化简

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

解答

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

求解步骤

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

使用法则:

(a) = a

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

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

使用指数法则:

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}

乘以共轭根式

\frac{- i}{- i}

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

化简

\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}}}

使用分式法则:

\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}}})

使用法则:

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}}}

使用分式法则:

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

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

使用法则:

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

流行的例子

化简 2e^{-9*2}

s im pl i f y 2 e^{- 9 \cdot 2}

化简-(sqrt(3))/(sqrt(5))

s im pl i f y - \frac{3}{5}

化简 \sqrt[4]{\sqrt[3]{j}}

s im pl i f y 4 3 j

化简 sqrt(\sqrt{729)}

s im pl i f y 729

展开 sqrt(4/9)sqrt(25/16)

e x p an d \frac{4}{9} \frac{25}{16}