Answer
$$4+3i^2-7i^3+10i^{12}=7i+11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4+3i^2-7i^3+10i^{12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4-3+7i+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7i+11\end{aligned} $$ | |
| ① | $$ 3i^2 = 3 \cdot (-1) = -3 $$ |
| ② | $$ -7i^3 = -7 \cdot \color{blue}{i^2} \cdot i =
-7 \cdot ( \color{blue}{-1}) \cdot i =
7 \cdot \, i $$ |
| ③ | $$ 10i^{12} = 10 \cdot i^{4 \cdot 3 + 0} =
10 \cdot \left( i^4 \right)^{ 3 } \cdot i^0 =
10 \cdot 1^{ 3 } \cdot 1 =
10 \cdot 1 $$ |
| ④ | Combine like terms: $$ 7i \color{blue}{-3} + \color{red}{4} + \color{red}{10} = 7i+ \color{red}{11} $$ |
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