vereinfachen (x+5)(3x-2)(x+2+i)(x-2+i)

Lösung

vereinfachen

(x + 5) (3 x - 2) (x + 2 + i) (x - 2 + i)

(x + 5) (3 x - 2) (x^{2} - 5) + (x + 5) (3 x - 2) \cdot 2 x i

Schritte zur Lösung

(x + 5) (3 x - 2) (x + 2 + i) (x - 2 + i)

Wende arithmetische Regel für komplexe Zahlen an:

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

= (x + 5) (3 x - 2) (((x + 2) (x - 2) - 1 \cdot 1) + ((x + 2) \cdot 1 + 1 \cdot (x - 2)) i)

Vereinfache

((x + 2) (x - 2) - 1 \cdot 1) + ((x + 2) \cdot 1 + 1 \cdot (x - 2)) i : (x^{2} - 5) + 2 x i

= (x + 5) (3 x - 2) ((x^{2} - 5) + 2 x i)

Setze Klammern

= (x + 5) (3 x - 2) (x^{2} - 5) + (x + 5) (3 x - 2) \cdot 2 x i

e x p an d 4 (6 x - 5 y = 28)

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

s im pl i f y (x + 1) (\frac{2 x}{x + 1} + 1)

e x p an d \frac{5 x + 13}{( 2 x + 1 ) ( x + 4 )}

e x p an d lo g_{10} (\frac{a - b}{a + b})