What is factor+e^{-inpi}-e^{inpi} ?

The solution to factor+e^{-inpi}-e^{inpi} is (cos(-pin)+isin(-pin))(1-cos(2pin)-isin(2pin))

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factor+e^{-inpi}-e^{inpi}

factor

+ e^{- inπ} - e^{inπ}

(cos (- πn) + i sin (- πn)) (1 - cos (2 πn) - i sin (2 πn))

Solution steps

e^{- inπ} - e^{inπ}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{inπ} = e^{- inπ} e^{2 inπ}

= e^{- inπ} - e^{- inπ} e^{2 inπ}

Factor out common term

e^{- inπ}

= e^{- inπ} (1 - e^{2 inπ})

Expand

- e^{2 iπn} + 1 : 1 - cos (2 πn) - i sin (2 πn)

= e^{- iπn} (1 - cos (2 πn) - i sin (2 πn))

Refine

= (cos (- πn) + i sin (- πn)) (1 - cos (2 πn) - i sin (2 πn))

2 (y)^{2 x}

(4 x - 1)^{3} + (x + 3)^{3}

3 - 2 - 64 p^{2}

\frac{x ^{3} - 64}{x - 4}

What is factor+e^{-inpi}-e^{inpi} ?
The solution to factor+e^{-inpi}-e^{inpi} is (cos(-pin)+isin(-pin))(1-cos(2pin)-isin(2pin))