What is expand e^x(x+iy)(cos(y)+isin(y)) ?

The solution to expand e^x(x+iy)(cos(y)+isin(y)) is (e^xxcos(y)-e^xysin(y))+i(e^xycos(y)+e^xxsin(y))

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expand e^x(x+iy)(cos(y)+isin(y))

expand

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

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

Solution steps

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

Expand

(x + i y) (cos (y) + i sin (y)) : (x cos (y) - y sin (y)) + i (y cos (y) + x sin (y))

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

Expand

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

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

(1 - y e^{x y}) \cdot (e^{- x y} + x)

\frac{5 e ^{- x}}{x ( x + 1 )}

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

(\frac{z - 1}{z T})^{2}

(e^{j θ} + e^{- j θ})^{3}

What is expand e^x(x+iy)(cos(y)+isin(y)) ?
The solution to expand e^x(x+iy)(cos(y)+isin(y)) is (e^xxcos(y)-e^xysin(y))+i(e^xycos(y)+e^xxsin(y))