What is expand (x+iy)^3 ?

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

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expand (x+iy)^3

expand

(x + i y)^{3}

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

Solution steps

(x + i y)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

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

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

Rewrite in standard complex form:

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

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

(3 x - x^{3}) (- 7 x + π) + e^{9} x

(6 - x) \cdot (6 + x)

(x + 2)^{4} (1 + \frac{1}{x ^{2}})

\frac{4}{7} + \frac{5}{14}

\frac{( 4 x ^{3} + 7 ) ^{5}}{( 12 x + 9 ) ^{2}}

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