What is e^{-2(x+yi)} ?

The solution to e^{-2(x+yi)} is e^{-2x}cos(2y)-ie^{-2x}sin(2y)

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simplify e^{-2(x+yi)}

simplify

e^{- 2 (x + y i)}

e^{- 2 x} cos (2 y) - i e^{- 2 x} sin (2 y)

Solution steps

e^{- 2 (x + y i)}

Apply imaginary number rule:

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

= e^{- 2 x} (cos (- 2 y) + i sin (- 2 y))

cos (- 2 y) = cos (2 y)

sin (- 2 y) i = - i sin (2 y)

= e^{- 2 x} (cos (2 y) - i sin (2 y))

Rewrite

e^{- 2 x} (cos (2 y) - i sin (2 y))

in standard complex form:

e^{- 2 x} cos (2 y) - e^{- 2 x} sin (2 y) i

= e^{- 2 x} cos (2 y) - e^{- 2 x} sin (2 y) i

6 (x^{2} + 2 x + 2)^{2}

\frac{5 x + 20}{( x + 2 ) ^{3}}

\frac{1}{( x - 7 ) x}

, (1 - D) \cdot (- V - I (R + Z))

\frac{5 q + 2 ( 1 + p ) ^{3}}{r + 3}

What is e^{-2(x+yi)} ?
The solution to e^{-2(x+yi)} is e^{-2x}cos(2y)-ie^{-2x}sin(2y)