What is expand (x+iy)^3+2(x+iy)^2-2(x+iy) ?

The solution to expand (x+iy)^3+2(x+iy)^2-2(x+iy) is (x^3-3xy^2+2x^2-2y^2-2x)+(3x^2y-y^3+4xy-2y)i

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

expand

(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

Solution steps

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

Expand

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

Expand

2 (x + i y)^{2} : 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)

Expand

- 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} + 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

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

36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30

(1 - x 2)^{2}

(x + i y) cos (x + i y)

7 (3 x + 2 y = - 7)

What is expand (x+iy)^3+2(x+iy)^2-2(x+iy) ?
The solution to expand (x+iy)^3+2(x+iy)^2-2(x+iy) is (x^3-3xy^2+2x^2-2y^2-2x)+(3x^2y-y^3+4xy-2y)i