What is expand (2+4i)^3 ?

The solution to expand (2+4i)^3 is -88-16i

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expand (2+4i)^3

expand

(2 + 4 i)^{3}

- 88 - 16 i

Solution steps

(2 + 4 i)^{3}

Apply Perfect Cube Formula:

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

(2 + 4 i)^{3} = 2^{3} + 3 \cdot 2^{2} \cdot 4 i + 3 \cdot 2 (4 i)^{2} + (4 i)^{3}

= 2^{3} + 3 \cdot 2^{2} \cdot 4 i + 3 \cdot 2 (4 i)^{2} + (4 i)^{3}

Simplify

2^{3} + 3 \cdot 2^{2} \cdot 4 i + 3 \cdot 2 (4 i)^{2} + (4 i)^{3} : - 16 i - 88

= - 16 i - 88

Rewrite in standard complex form:

- 88 - 16 i

= - 88 - 16 i

\frac{4 ( 6 + 3 )}{33}

- 2 (2 + 34)

\frac{( - n ^{2} - 3 n )}{2 ( 1 - 2 n )}

\frac{( 2 x ^{3} - 4 x ^{2} - 15 x + 4 )}{( x - 1 ) ^{2}}

(t^{2} e^{- t} - 4 t e^{- t} + 2 e^{- t})^{2} e^{t}