Question
Answer
$$(-5x+5i)(3i)^3=135ix-(-135)$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-5x+5i)(3i)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-5x+5i)\cdot27i^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-5x+5i)\cdot-27i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}135ix-135i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}135ix-(-135)\end{aligned} $$ | |
| 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 | $$ \left( \color{blue}{-5x+5i}\right) \cdot -27i = 135ix-135i^2 $$ |
| ④ | $$ 135i^2 = 135 \cdot (-1) = -135 $$ |
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