What is e^{(-a-iw)*2} ?

The solution to e^{(-a-iw)*2} is e^{-2a}cos(2w)-ie^{-2a}sin(2w)

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simplify e^{(-a-iw)*2}

simplify

e^{(- a - i w) \cdot 2}

e^{- 2 a} cos (2 w) - i e^{- 2 a} sin (2 w)

Solution steps

e^{(- a - i w) \cdot 2}

Apply imaginary number rule:

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

= e^{- 2 a} (cos (- 2 w) + i sin (- 2 w))

cos (- 2 w) = cos (2 w)

sin (- 2 w) i = - i sin (2 w)

= e^{- 2 a} (cos (2 w) - i sin (2 w))

Rewrite

e^{- 2 a} (cos (2 w) - i sin (2 w))

in standard complex form:

e^{- 2 a} cos (2 w) - e^{- 2 a} sin (2 w) i

= e^{- 2 a} cos (2 w) - e^{- 2 a} sin (2 w) i

\frac{( 1 + 2 x ) ^{2}}{( ( 2 - x ) ( 3 - 3 x ) ^{2} )}

(ln (y - 2) + \frac{x - 3}{y - 2} = C) y - 2

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{3} - 7 x^{2} + 3 x - 9))

(6, - 8, 3) y (- 4, - 1, - 3)

\frac{0.8 ( 1.5 P + 1.5 T )}{P}

What is e^{(-a-iw)*2} ?
The solution to e^{(-a-iw)*2} is e^{-2a}cos(2w)-ie^{-2a}sin(2w)