vereinfachen c*e^{(1+3i)x}x+c_{0}e^{(1-3i)x}

Lösung

vereinfachen

c \cdot e^{(1 + 3 i) x} x + c_{0} e^{(1 - 3 i) x}

(c e^{x} x cos (3 x) + c_{0} e^{x} cos (3 x)) + i (- c_{0} e^{x} sin (3 x) + c e^{x} x sin (3 x))

Schritte zur Lösung

c e^{(1 + 3 i) x} x + c_{0} e^{(1 - 3 i) x}

e^{(1 + 3 i) x} = e^{x} (cos (3 x) + i sin (3 x))

= c e^{x} x (cos (3 x) + i sin (3 x)) + c_{0} e^{(1 - 3 i) x}

e^{(1 - 3 i) x} = e^{x} (cos (3 x) - i sin (3 x))

= c e^{x} x (cos (3 x) + i sin (3 x)) + c_{0} e^{x} (cos (3 x) - i sin (3 x))

Schreibe

c e^{x} (cos (3 x) + sin (3 x) i) x + c_{0} e^{x} (cos (3 x) - i sin (3 x))

in der Standard komplexen Form um:

(c e^{x} x cos (3 x) + c_{0} e^{x} cos (3 x)) + (c e^{x} x sin (3 x) - c_{0} e^{x} sin (3 x)) i

= (c e^{x} x cos (3 x) + c_{0} e^{x} cos (3 x)) + (c e^{x} x sin (3 x) - c_{0} e^{x} sin (3 x)) i

e x p an d \frac{x - 3}{x ^{2} ( x - 5 )}

e x p an d \frac{( 1 + cos ( x ) ) ^{2}}{2}

e x p an d \frac{2 ( 3 - 6 )}{3}

e x p an d (1 + \frac{π}{2}) (π - \frac{π}{2})

e x p an d 2 (22500 ln (1968300000000) - 200)