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Popular >

simplify (-i)^{-5}

Solution

simplify

(- i)^{- 5}

Solution

i

Solution steps

(- i)^{- 5}

Apply exponent rule:

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

(- i)^{- 5} = \frac{1}{( - i ) ^{5}}

= \frac{1}{( - i ) ^{5}}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

(- i)^{5} = - i^{5}

= \frac{1}{- i ^{5}}

Simplify

i^{5} : 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}

Simplify

\frac{- i}{- 1} : i

= i

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Frequently Asked Questions (FAQ)

What is (-i)^{-5} ?
The solution to (-i)^{-5} is i