Question
Answer
$$(0.664+0.331i)^3=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(0.664+0.331i)^3& \xlongequal{ }(0.664+0i)^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0+0i+0i^2+0i^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0\end{aligned} $$ | |
| ① | Find $ \left(0+0i\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 0 $ and $ B = 0i $. $$ \left(0+0i\right)^3 = 0^3+3 \cdot 0^2 \cdot 0i + 3 \cdot 0 \cdot \left( 0i \right)^2+\left( 0i \right)^3 = 00i0i^20i^3 $$ |
| ② | Combine like terms: $$ 0 = 0 $$ |
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