Answer
$$(4i^9-8i^3)(8i^6-6i^8)=-168i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4i^9-8i^3)(8i^6-6i^8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(4i+8i)\cdot(-8-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12i\cdot(-14) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-168i\end{aligned} $$ | |
| ① | $$ 4i^9 = 4 \cdot i^{4 \cdot 2 + 1} =
4 \cdot \left( i^4 \right)^{ 2 } \cdot i^1 =
4 \cdot 1^{ 2 } \cdot i =
4 \cdot i $$ |
| ② | $$ -8i^3 = -8 \cdot \color{blue}{i^2} \cdot i =
-8 \cdot ( \color{blue}{-1}) \cdot i =
8 \cdot \, i $$$$ 8i^6 = 8 \cdot i^{4 \cdot 1 + 2} =
8 \cdot \left( i^4 \right)^{ 1 } \cdot i^2 =
8 \cdot 1^{ 1 } \cdot (-1) =
8 \cdot -1 = -8 $$ |
| ③ | $$ -6i^8 = -6 \cdot i^{4 \cdot 2 + 0} =
-6 \cdot \left( i^4 \right)^{ 2 } \cdot i^0 =
-6 \cdot 1^{ 2 } \cdot 1 =
-6 \cdot 1 $$ |
| ④ | Combine like terms: $$ \color{blue}{4i} + \color{blue}{8i} = \color{blue}{12i} $$Combine like terms: $$ \color{blue}{-8} \color{blue}{-6} = \color{blue}{-14} $$ |
| ⑤ | $$ 12 i \cdot -14 = -168 i $$ |
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