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

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

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

simplify

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

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

Solution steps

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

= (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 ii y - y^{2} x - y^{2} i y

Simplify

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

(2, - 3) y (1, 1)

(x + 1 + 3)^{2}

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

(1 - cos (x)) (1 + sec (x)) cos (x)

3 e^{2 (1 + iπ)}

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