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

The solution to expand (3+2i)^3 is -9+46i

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expand (3+2i)^3

expand

(3 + 2 i)^{3}

- 9 + 46 i

Solution steps

(3 + 2 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

3^{3} + 3 \cdot 3^{2} \cdot 2 i + 3 \cdot 3 (2 i)^{2} + (2 i)^{3} : 46 i - 9

= 46 i - 9

Rewrite in standard complex form:

- 9 + 46 i

= - 9 + 46 i

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