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

The solution to (x+yi)(x-yi)^2 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+yi)(x-yi)^2

simplify

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

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

Solution steps

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

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

Expand

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

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

Distribute parentheses

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

Simplify

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

arcsec (1)

\frac{( a + b ) ^{2}}{2}

2 y - 3 + 6 y - 2 x

2 (3 - 2)

t (e^{t} + e^{2 t})

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