What is (a+bi)(a-bi)^2 ?

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

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simplify (a+bi)(a-bi)^2

simplify

(a + bi) (a - bi)^{2}

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

Solution steps

(a + bi) (a - bi)^{2}

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

Expand

(a - bi)^{2} : a^{2} - 2 abi - b^{2}

= (a^{2} - 2 abi - b^{2}) (a + bi)

Distribute parentheses

= a^{2} a + a^{2} bi - 2 abia - 2 abibi - b^{2} a - b^{2} bi

Simplify

a^{2} a + a^{2} bi - 2 abia - 2 abibi - b^{2} a - b^{2} bi : a^{3} - a^{2} bi + a b^{2} - i b^{3}

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

Rewrite in standard complex form:

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

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

e^{3 x} (9 - x)

(- 2, 4) y (5, - 3)

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

[8 (a + b) + 6 (- z - y)] [8 (a + b) + 6 (y + z)]

4 (3 - 1)

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