What is expand e^{(x+yi)^2} ?

The solution to expand e^{(x+yi)^2} is e^{x^2-y^2}cos(2xy)+ie^{x^2-y^2}sin(2xy)

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

expand

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

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

Solution steps

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

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

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

Apply imaginary number rule:

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x^{2} - y^{2}}, b = cos (2 x y), c = sin (2 x y) i

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

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

\frac{2 s - 7}{( s - 4 ) ( s + 5 )}

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

(- 1, - 2) y (0, 0)

, (2 - x r i g h t)

2 tan (4) (x - 8)

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