vereinfachen xi(xi+1)(xi+3)

Lösung

vereinfachen

x i \cdot (x i + 1) \cdot (x i + 3)

- 4 x^{2} + (3 x - x^{3}) i

Schritte zur Lösung

x i (x i + 1) (x i + 3)

Schreibe

x i + 1

in der Standard komplexen Form um:

1 + x i

Schreibe

x i + 3

in der Standard komplexen Form um:

3 + x i

= x i (1 + x i) (3 + x i)

Wende arithmetische Regel für komplexe Zahlen an:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= x i ((1 \cdot 3 - xx) + (1 \cdot x + x \cdot 3) i)

Vereinfache

(1 \cdot 3 - xx) + (1 \cdot x + x \cdot 3) i : (3 - x^{2}) + 4 x i

= x i ((3 - x^{2}) + 4 x i)

Schreibe

x i ((3 - x^{2}) + 4 x i)

um:

3 x i - x^{3} i - 4 x^{2}

= 3 x i - x^{3} i - 4 x^{2}

Rewrite in standard complex form:

- 4 x^{2} + (3 x - x^{3}) i

= - 4 x^{2} + (3 x - x^{3}) i

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

\frac{d}{d y} ((x) (6 x^{3} + 2 x + 9))

e x p an d 4 (\frac{32}{π} - \frac{256}{π ^{3}})

e x p an d \frac{( 5 x - 8 ) ^{2} x ( 3 + x ) ( 3 - x )}{25}

e x p an d (4 x^{2} - \frac{3}{x})^{5}