展开 (x+iy)^3-2(x+iy)+6

解答

展开

(x + i y)^{3} - 2 (x + i y) + 6

(x^{3} - 3 x y^{2} - 2 x + 6) + (3 x^{2} y - y^{3} - 2 y) i

求解步骤

(x + i y)^{3} - 2 (x + i y) + 6

展开

(x + i y)^{3} : 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) + 6

展开

- 2 (x + i y) : - 2 x - 2 y i

= x^{3} + 3 x^{2} y i - 3 x y^{2} - i y^{3} - 2 x - 2 y i + 6

Rewrite in standard complex form:

(x^{3} - 3 x y^{2} - 2 x + 6) + (3 x^{2} y - y^{3} - 2 y) i

= (x^{3} - 3 x y^{2} - 2 x + 6) + (3 x^{2} y - y^{3} - 2 y) i

e x p an d (x - 1 + i) (x - 1 - i)

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

e x p an d - \frac{8 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

e x p an d - 6 y l e f t (5 y^{2} - 4 y + 2)

e x p an d \frac{x ^{2} + 1}{( x ^{3} - 5 x ^{2} - 6 x ) ( x ^{2} + x + 9 )}