erweitern ((a+i)^5)/((1-i)^3)

Lösung

erweitern

\frac{( a + i ) ^{5}}{( 1 - i ) ^{3}}

\frac{a ^{5} + 5 a ^{4} i + 10 a ^{3} i ^{2} + 10 a ^{2} i ^{3} + 5 a i ^{4} + i ^{5}}{1 - 3 i + 3 i ^{2} - i ^{3}}

Schritte zur Lösung

\frac{( a + i ) ^{5}}{( 1 - i ) ^{3}}

(1 - i)^{3} = 1 - 3 i + 3 i^{2} - i^{3}

= \frac{( a + i ) ^{5}}{1 - 3 i + 3 i ^{2} - i ^{3}}

(a + i)^{5} = a^{5} + 5 a^{4} i + 10 a^{3} i^{2} + 10 a^{2} i^{3} + 5 a i^{4} + i^{5}

= \frac{a ^{5} + 5 a ^{4} i + 10 a ^{3} i ^{2} + 10 a ^{2} i ^{3} + 5 a i ^{4} + i ^{5}}{1 - 3 i + 3 i ^{2} - i ^{3}}

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

e x p an d \frac{( 1 - 2 y ) ^{2}}{2}

e x p an d 11 (10 + 3)

e x p an d \frac{x + 2}{2 - x - 12} + \frac{x - 1}{2 + 2 x}

e x p an d t^{2} e^{4 t^{5}} (3 - 20 t^{5} - 40 t^{2})