erweitern (a+bi)/((a-bi)^2)

Lösung

erweitern

\frac{a + bi}{( a - bi ) ^{2}}

\frac{a ^{3} - 3 a b ^{2}}{a ^{4} + b ^{4} + 2 a ^{2} b ^{2}} + i \frac{- b ^{3} + 3 a ^{2} b}{a ^{4} + b ^{4} + 2 a ^{2} b ^{2}}

Schritte zur Lösung

\frac{a + bi}{( a - bi ) ^{2}}

(a - bi)^{2} = a^{2} - 2 iab - b^{2}

= \frac{a + ib}{a ^{2} - 2 iab - b ^{2}}

Rationalisiere

\frac{a + ib}{a ^{2} - 2 iab - b ^{2}} : \frac{a ^{3} - 3 a b ^{2} + i ( - b ^{3} + 3 a ^{2} b )}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}}

= \frac{a ^{3} - 3 a b ^{2} + i ( - b ^{3} + 3 a ^{2} b )}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}}

Schreibe

\frac{a ^{3} - 3 a b ^{2} + i ( 3 a ^{2} b - b ^{3} )}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}}

in der Standard komplexen Form um:

\frac{a ^{3} - 3 a b ^{2}}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}} + \frac{3 a ^{2} b - b ^{3}}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}} i

= \frac{a ^{3} - 3 a b ^{2}}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}} + \frac{3 a ^{2} b - b ^{3}}{a ^{4} + 2 a ^{2} b ^{2} + b ^{4}} i

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

e x p an d y (a - b y^{2}) d y

e x p an d 7 pp

e x p an d y Q_{0} (1 - e^{- \frac{y}{a}})

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