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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x+iy)^2(x-iy)

simplify

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

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

Solution steps

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

Expand

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

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

Distribute parentheses

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

Simplify

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

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

Rewrite in standard complex form:

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

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

(x^{3} + y^{3}) d x

\frac{2 x ^{2} + 1}{( x - 3 ) ^{2}}

2 (e - 1)

(- 3 + i)^{6}

\frac{1}{( k + 1 ) ( k + 2 )}

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