Question
Answer
$$5i(-2i)^3=-40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5i(-2i)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5i\cdot-8i^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5i\cdot8i \xlongequal{ } \\[1 em] & \xlongequal{ }40i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-40\end{aligned} $$ | |
| ① | $$ \left( -2i \right)^3 = (-2)^3i^3 = -8i^3 $$ |
| ② | $$ -8i^3 = -8 \cdot \color{blue}{i^2} \cdot i =
-8 \cdot ( \color{blue}{-1}) \cdot i =
8 \cdot \, i $$ |
| ③ | $$ 40i^2 = 40 \cdot (-1) = -40 $$ |
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