erweitern (x+iy)^3+2(x+iy)^2-2(x+iy)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Schreibe

(x + i y)^{3}

um:

x^{3} + 3 x^{2} y i - 3 x y^{2} - i y^{3}

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

Schreibe

2 (x + i y)^{2}

um:

2 x^{2} + 4 x y i - 2 y^{2}

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

Schreibe

- 2 (x + i y)

um:

- 2 x - 2 y i

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

Rewrite in standard complex form:

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

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

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

e x p an d 36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30

s im pl i f y (1 - x 2)^{2}

s im pl i f y (x + i y) cos (x + i y)

e x p an d 7 (3 x + 2 y = - 7)