simplify (θ+wi)^3

Solution

simplify

(θ + w i)^{3}

(θ^{3} - 3 θ w^{2}) + (3 θ^{2} w - w^{3}) i

Solution steps

(θ + w i)^{3}

Apply Perfect Cube Formula:

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

(θ + w i)^{3} = θ^{3} + 3 θ^{2} w i + 3 θ (w i)^{2} + (w i)^{3}

= θ^{3} + 3 θ^{2} w i + 3 θ (w i)^{2} + (w i)^{3}

3 θ (w i)^{2} = - 3 θ w^{2}

(w i)^{3} = - i w^{3}

= θ^{3} + 3 θ^{2} w i - 3 θ w^{2} - i w^{3}

Rewrite in standard complex form:

(θ^{3} - 3 θ w^{2}) + (3 θ^{2} w - w^{3}) i

= (θ^{3} - 3 θ w^{2}) + (3 θ^{2} w - w^{3}) i

\frac{( - 2 )}{2}

(u + 2) (u + 5)

- 7 x^{5} y^{3} (- 5 x^{4} y^{4})

\frac{5}{6} \div 10

(- 2 x - 11)^{2} + 5 (- 2 x - 11) + 6