vereinfachen (x+i)(x-8+i)(x-8-i)

Lösung

vereinfachen

(x + i) (x - 8 + i) (x - 8 - i)

(x^{3} - 16 x^{2} + 65 x) + (x^{2} - 16 x + 65) i

Schritte zur Lösung

(x + i) (x - 8 + i) (x - 8 - i)

Schreibe

x - 8 - i

in der Standard komplexen Form um:

(x - 8) - i

= (x + i) (x - 8 + i) ((x - 8) - i)

Wende arithmetische Regel für komplexe Zahlen an:

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

= ((x (x - 8) - 1 \cdot 1) + (x \cdot 1 + 1 \cdot (x - 8)) i) ((x - 8) - i)

Wende arithmetische Regel für komplexe Zahlen an:

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

= ((x (x - 8) - 1 \cdot 1) (x - 8) - (x \cdot 1 + 1 \cdot (x - 8)) (- 1)) + ((x (x - 8) - 1 \cdot 1) (- 1) + (x \cdot 1 + 1 \cdot (x - 8)) (x - 8)) i

Vereinfache

((x (x - 8) - 1 \cdot 1) (x - 8) - (x \cdot 1 + 1 \cdot (x - 8)) (- 1)) + ((x (x - 8) - 1 \cdot 1) (- 1) + (x \cdot 1 + 1 \cdot (x - 8)) (x - 8)) i : (x^{3} - 16 x^{2} + 65 x) + (x^{2} - 16 x + 65) i

= (x^{3} - 16 x^{2} + 65 x) + (x^{2} - 16 x + 65) i

e x p an d 4 sin (\frac{π}{4})

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

e x p an d \frac{13 ( s + 2 )}{s ( s + 8 ) ( s + 1 )}

e x p an d \frac{12.9282 ( 0.25 x ^{2} - 1 )}{2 + 0.44758 x ^{2}}

e x p an d 2 (sin (x) + x cos (x)) (2 cos (x) - x sin (x))