erweitern ((x-iy)^2)/(x^2+y^2)

Lösung

erweitern

\frac{( x - i y ) ^{2}}{x ^{2} + y ^{2}}

\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - i \frac{2 x y}{x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{( x - i y ) ^{2}}{x ^{2} + y ^{2}}

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

= \frac{x ^{2} - 2 i x y - y ^{2}}{x ^{2} + y ^{2}}

Schreibe

\frac{x ^{2} - 2 i x y - y ^{2}}{x ^{2} + y ^{2}}

in der Standard komplexen Form um:

\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - \frac{2 x y}{x ^{2} + y ^{2}} i

= \frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}} - \frac{2 x y}{x ^{2} + y ^{2}} i

s im pl i f y e^{2 (x + y i)}

e x p an d \frac{x ( x + 1 ) ( x + 2 )}{6}

e x p an d \frac{π ( e ^{3} - 1 )}{3 e ^{3}}

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

e x p an d (2 x^{3} - 4 x^{2} + 1)^{5}