What is x(e^{iy}+e^{i2piy}) ?

The solution to x(e^{iy}+e^{i2piy}) is (xcos(y)+xcos(2piy))+i(xsin(2piy)+xsin(y))

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simplify x(e^{iy}+e^{i2piy})

simplify

x (e^{i y} + e^{i 2 π y})

(x cos (y) + x cos (2 π y)) + i (x sin (2 π y) + x sin (y))

Solution steps

x (e^{i y} + e^{i 2 π y})

Apply imaginary number rule:

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

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

Apply imaginary number rule:

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

= x (cos (y) + i sin (y) + cos (2 π y) + i sin (2 π y))

Rewrite

x (cos (y) + sin (y) i + cos (2 π y) + sin (2 π y) i)

in standard complex form:

(x cos (y) + x cos (2 π y)) + (x sin (y) + x sin (2 π y)) i

= (x cos (y) + x cos (2 π y)) + (x sin (y) + x sin (2 π y)) i

\frac{1}{( s + a ) ( s + b ) ^{2}}

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

3 (11 + 2)

(x - 3)^{3}

\frac{1 - e ^{- 2 π s}}{( s ^{2} + 1 ) ( s ^{2} + 4 )}

What is x(e^{iy}+e^{i2piy}) ?
The solution to x(e^{iy}+e^{i2piy}) is (xcos(y)+xcos(2piy))+i(xsin(2piy)+xsin(y))