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Popular >

simplify ((e^{zi}-e^{-iz}))^3

Solution

simplify

((e^{z i} - e^{- i z}))^{3}

Solution

- 8 i sin^{3} (z)

Solution steps

(e^{z i} - e^{- i z})^{3}

e^{z i} = cos (z) + i sin (z)

e^{- i z} = cos (z) - i sin (z)

= (cos (z) + i sin (z) - (cos (z) - i sin (z)))^{3}

Expand

cos (z) + sin (z) i - (cos (z) - i sin (z)) : 2 i sin (z)

= (2 i sin (z))^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{3} i^{3} sin^{3} (z)

2^{3} = 8

= 8 i^{3} sin^{3} (z)

i^{3} = - i

= 8 (- i) sin^{3} (z)

Remove parentheses:

(- a) = - a

= - 8 i sin^{3} (z)

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Frequently Asked Questions (FAQ)

What is ((e^{zi}-e^{-iz}))^3 ?
The solution to ((e^{zi}-e^{-iz}))^3 is -8isin^3(z)