What is expand (a+bi)^3 ?

The solution to expand (a+bi)^3 is (a^3-3ab^2)+(3a^2b-b^3)i

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expand (a+bi)^3

expand

(a + bi)^{3}

(a^{3} - 3 a b^{2}) + (3 a^{2} b - b^{3}) i

Solution steps

(a + bi)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

a^{3} + 3 a^{2} bi + 3 a (bi)^{2} + (bi)^{3} : a^{3} + 3 a^{2} bi - 3 a b^{2} - i b^{3}

= a^{3} + 3 a^{2} bi - 3 a b^{2} - i b^{3}

Rewrite in standard complex form:

(a^{3} - 3 a b^{2}) + (3 a^{2} b - b^{3}) i

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

35 (22 + 33 + 47)

(z + i)^{2}

2 (7 - 35)

- x t + x (e^{\frac{t}{x}} + 1)

I n (x + 1 + x^{2})

What is expand (a+bi)^3 ?
The solution to expand (a+bi)^3 is (a^3-3ab^2)+(3a^2b-b^3)i