Question
Answer
$$3i^5-i^4+7i^3-10i^2-9=-4i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3i^5-i^4+7i^3-10i^2-9& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3i-1-7i+10-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-4i\end{aligned} $$ | |
| ① | $$ 3i^5 = 3 \cdot i^{4 \cdot 1 + 1} =
3 \cdot \left( i^4 \right)^{ 1 } \cdot i^1 =
3 \cdot 1^{ 1 } \cdot i =
3 \cdot i $$ |
| ② | $$ -i^4 = - i^2 \cdot i^2 =
- ( - 1) \cdot ( - 1) =
-1 $$ |
| ③ | $$ 7i^3 = 7 \cdot \color{blue}{i^2} \cdot i =
7 \cdot ( \color{blue}{-1}) \cdot i =
-7 \cdot \, i $$ |
| ④ | $$ -10i^2 = -10 \cdot (-1) = 10 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3i} \color{blue}{-7i} \color{red}{-1} + \color{green}{10} \color{green}{-9} = \color{blue}{-4i} $$ |
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