What is e^{2(x+iy)+i} ?

The solution to e^{2(x+iy)+i} is e^{2x}cos(1+2y)+ie^{2x}sin(1+2y)

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simplify e^{2(x+iy)+i}

simplify

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

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

Solution steps

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

Apply imaginary number rule:

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

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

Rewrite

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

in standard complex form:

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

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

\frac{- 1 - 131}{6}

\frac{( x - 3 ) ( x - 4 )}{6}

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

\frac{x + 4}{( x - 7 ) ( x + 3 )}

\frac{( x + 5 ) ^{2}}{x ^{2} + 25}

What is e^{2(x+iy)+i} ?
The solution to e^{2(x+iy)+i} is e^{2x}cos(1+2y)+ie^{2x}sin(1+2y)