Question
Answer
$$(2x+3i)(-3i)^3=54ix+(-81)$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+3i)(-3i)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+3i)\cdot-27i^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x+3i)\cdot27i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}54ix+81i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}54ix+(-81)\end{aligned} $$ | |
| ① | $$ \left( -3i \right)^3 = (-3)^3i^3 = -27i^3 $$ |
| ② | $$ -27i^3 = -27 \cdot \color{blue}{i^2} \cdot i =
-27 \cdot ( \color{blue}{-1}) \cdot i =
27 \cdot \, i $$ |
| ③ | $$ \left( \color{blue}{2x+3i}\right) \cdot 27i = 54ix+81i^2 $$ |
| ④ | $$ 81i^2 = 81 \cdot (-1) = -81 $$ |
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