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Popular >

simplify e^{((2+3i)pi)/2}

Solution

simplify

e^{\frac{( 2 + 3 i ) π}{2}}

Solution

- i e^{π}

Solution steps

e^{\frac{( 2 + 3 i ) π}{2}}

Apply imaginary number rule:

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

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

cos (\frac{3 π}{2}) = 0

sin (\frac{3 π}{2}) i = - i

= e^{π} (0 - i)

0 - i = - i

= (- i) e^{π}

Remove parentheses:

(- a) = - a

= - e^{π} i

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Frequently Asked Questions (FAQ)

What is e^{((2+3i)pi)/2} ?
The solution to e^{((2+3i)pi)/2} is -ie^pi