What is ((-1)/2)^{(-1)/2} ?

The solution to ((-1)/2)^{(-1)/2} is -2^{1/2}i

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simplify ((-1)/2)^{(-1)/2}

simplify

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

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

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

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

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

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

Simplify

\frac{\frac{1}{i}}{\frac{1}{2 ^{\frac{1}{2}}}} : \frac{2 ^{\frac{1}{2}}}{i}

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

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

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

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

Apply the fraction rule:

\frac{a}{1} = a

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

14 - \frac{1}{7}

(4 - 2 i) - (- 1 + 3 i)

(- 21 + 19 i) - (- 10 - 5 i)

\frac{25}{7}

\frac{- 180}{- 10}