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))

Rewrite

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

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

\frac{x ( x + 1 ) ( x + 2 )}{6}

\frac{π ( e ^{3} - 1 )}{3 e ^{3}}

(4 a^{2} - 3 b + 2 c d - 5 e)^{2}

(2 x^{3} - 4 x^{2} + 1)^{5}

π (4 x - 3)^{2}

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