What is e^{-sqrt(-1)(3/4)pi} ?

The solution to e^{-sqrt(-1)(3/4)pi} is -i(sqrt(2))/2-(sqrt(2))/2

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simplify e^{-sqrt(-1)(3/4)pi}

simplify

e^{- - 1 (\frac{3}{4}) π}

- i \frac{2}{2} - \frac{2}{2}

Solution steps

e^{- - 1 (\frac{3}{4}) π}

Apply exponent rule:

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

= \frac{1}{e ^{- 1 π \frac{3}{4}}}

e^{- 1 \frac{3}{4} π} = e^{iπ \frac{3}{4}}

= \frac{1}{e ^{iπ \frac{3}{4}}}

e^{i \frac{3}{4} π} = \frac{- 1 + i}{2}

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Rationalize

\frac{2}{- 1 + i} : \frac{- 1 - i}{2}

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

Rewrite

\frac{- 1 - i}{2}

in standard complex form:

- \frac{2}{2} - \frac{2}{2} i

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

(4.5 x 1 0^{5}) (8.3 x 1 0^{1})

(B^{3} C^{4})^{5}

2 y (2 y^{3})

2.9 \cdot 1 0^{- 4} \cdot 10000

0.053 \cdot 5.4 \cdot 1 0^{- 2}

What is e^{-sqrt(-1)(3/4)pi} ?
The solution to e^{-sqrt(-1)(3/4)pi} is -i(sqrt(2))/2-(sqrt(2))/2