What is 1/(sqrt(-1)) ?

The solution to 1/(sqrt(-1)) is -i

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simplify 1/(sqrt(-1))

simplify

\frac{1}{- 1}

- i

Solution steps

\frac{1}{- 1}

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

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