Answer
$$(x+iy)^3=i^3y^3+3i^2xy^2+3ix^2y+x^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+iy)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3+3ix^2y+3i^2xy^2+i^3y^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}i^3y^3+3i^2xy^2+3ix^2y+x^3\end{aligned} $$ | |
| ① | Find $ \left(x+iy\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x $ and $ B = iy $. $$ \left(x+iy\right)^3 = x^3+3 \cdot x^2 \cdot iy + 3 \cdot x \cdot \left( iy \right)^2+\left( iy \right)^3 = x^3+3ix^2y+3i^2xy^2+i^3y^3 $$ |
| ② | Combine like terms: $$ i^3y^3+3i^2xy^2+3ix^2y+x^3 = i^3y^3+3i^2xy^2+3ix^2y+x^3 $$ |
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