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Popular >

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

Solution

simplify

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

Solution

- i

Solution steps

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

Apply exponent rule:

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

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

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

Apply imaginary number rule:

- 1 = i

= \frac{1}{i}

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

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

= \frac{- i}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - i

Popular Examples

(5.972*10^{24})(3.83*10^5-x)^2=x^2*(7.35*10^{22})

(5.972 \cdot 1 0^{24}) (3.83 \cdot 1 0^{5} - x)^{2} = x^{2} \cdot (7.35 \cdot 1 0^{22})

simplify 1/2 x^{-2}simplify

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

3 x^{2} - 12 x = 9

- 3 c + 15 = 3

simplify ((a+b)^9)/((a+b)^4)simplify

\frac{( a + b ) ^{9}}{( a + b ) ^{4}}

Frequently Asked Questions (FAQ)

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