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Popular >

simplify e^{-i(pi/2)}

Solution

simplify

e^{- i (\frac{π}{2})}

Solution

- i

Solution steps

e^{- i (\frac{π}{2})}

Remove parentheses:

(a) = a

= e^{- i \frac{π}{2}}

Multiply

- i \frac{π}{2} : - \frac{πi}{2}

= e^{- \frac{πi}{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^{-i(pi/2)} ?
The solution to e^{-i(pi/2)} is -i