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

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

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simplify (x+iy)^3+(x+iy)^2

simplify

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

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

Solution steps

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

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

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

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

Rewrite in standard complex form:

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

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

(sin (x) + 2 cos (x))^{2}

\frac{( - x + 5 ) ( x + 1 )}{2}

(z - 6 i)^{2}

\frac{( x - 6 ) ^{4}}{81}

6 (- 1)^{5} - 24 (- 1)^{3} + 18 (- 1)

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