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Popular >

simplify e^{(-ipi)/2}

Solution

simplify

e^{\frac{- iπ}{2}}

Solution

- i

Solution steps

e^{\frac{- iπ}{2}}

Apply the fraction rule:

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

= e^{- \frac{iπ}{2}}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

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

cos (- \frac{π}{2}) = 0

sin (- \frac{π}{2}) = - 1

0 - 1 i = - 1 i

= - 1 i

Multiply:

1 i = i

= - i

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Frequently Asked Questions (FAQ)

What is e^{(-ipi)/2} ?
The solution to e^{(-ipi)/2} is -i