What is factor e^{x+yi}+e^{-x-yi} ?

The solution to factor e^{x+yi}+e^{-x-yi} is e^{-x}(cos(-y)+isin(-y))(e^{2x}(cos(2y)+isin(2y))+1)

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factor e^{x+yi}+e^{-x-yi}

factor

e^{x + y i} + e^{- x - y i}

e^{- x} (cos (- y) + i sin (- y)) (e^{2 x} (cos (2 y) + i sin (2 y)) + 1)

Solution steps

e^{x + y i} + e^{- x - y i}

Apply exponent rule:

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

= e^{x} e^{i y} + e^{- x} e^{- i y}

Apply exponent rule:

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

e^{x} = e^{- x} e^{2 x}, e^{i y} = e^{- i y} e^{2 i y}

= e^{- x} e^{2 x} e^{- i y} e^{2 i y} + e^{- x} e^{- i y}

Factor out common term

e^{- i y} e^{- x}

= e^{- i y} e^{- x} (e^{2 x} e^{2 i y} + 1)

Refine

= e^{- x} (cos (- y) + i sin (- y)) (e^{2 x} (cos (2 y) + i sin (2 y)) + 1)

4 = 0.25 (w - 4.3)

8 + \frac{1}{3}

2 (- \frac{2}{7})^{0}

8 a^{2} + 2 a - 6

(16)^{\frac{3}{4}}

What is factor e^{x+yi}+e^{-x-yi} ?
The solution to factor e^{x+yi}+e^{-x-yi} is e^{-x}(cos(-y)+isin(-y))(e^{2x}(cos(2y)+isin(2y))+1)