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Popular >

simplify e^{-3pii}

Solution

simplify

e^{- 3 πi}

Solution

- 1

Solution steps

e^{- 3 πi}

Apply imaginary number rule:

e^{iaπ} = (- 1)^{a}

= (- 1)^{- 3}

Apply exponent rule:

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

= \frac{1}{( - 1 ) ^{3}}

Apply exponent rule:

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

if

n

is odd

(- 1)^{3} = - 1^{3}

= \frac{1}{- 1 ^{3}}

Apply the fraction rule:

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

= - \frac{1}{1 ^{3}}

Simplify

= - 1

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Frequently Asked Questions (FAQ)

What is e^{-3pii} ?
The solution to e^{-3pii} is -1