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simplify e^{-sqrt((3(-1))/2)}

Solution

simplify

e^{- \frac{3 ( - 1 )}{2}}

Solution

- i \frac{sin ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )} + \frac{cos ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )}

Solution steps

e^{- \frac{3 ( - 1 )}{2}}

Apply exponent rule:

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

= \frac{1}{e ^{\frac{3 ( - 1 )}{2}}}

Remove parentheses:

(- a) = - a

= \frac{1}{e ^{\frac{- 3 \cdot 1}{2}}}

e^{\frac{- 3 \cdot 1}{2}} = e^{i \frac{3}{2}}

= \frac{1}{e ^{i \frac{3}{2}}}

e^{i \frac{3}{2}} = cos (\frac{3}{2}) + i sin (\frac{3}{2})

= \frac{1}{cos ( \frac{3}{2} ) + i sin ( \frac{3}{2} )}

Rationalize

\frac{1}{cos ( \frac{3}{2} ) + i sin ( \frac{3}{2} )} : \frac{- i sin ( \frac{3}{2} ) + cos ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )}

= \frac{cos ( \frac{3}{2} ) - i sin ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )}

Rewrite

\frac{cos ( \frac{3}{2} ) - sin ( \frac{3}{2} ) i}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )}

in standard complex form:

\frac{cos ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )} - \frac{sin ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )} i

= \frac{cos ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )} - \frac{sin ( \frac{3}{2} )}{cos ^{2} ( \frac{3}{2} ) + sin ^{2} ( \frac{3}{2} )} i

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Frequently Asked Questions (FAQ)

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