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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

Rewrite in standard complex form:

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

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

⌈ 1.5 ⌉

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

(x - 2 - 2 i) (x - 2 + 2 i)

\frac{4}{9} + \frac{5}{6} - \frac{7}{18}

\frac{3}{5} \times 40

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