Question
Answer
$$2^3+2^2i+3\cdot2i^2+i^3=3i+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2^3+2^2i+3\cdot2i^2+i^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2^3+2^2i+3\cdot(-2)-i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2^3+2^2i+(-6)-i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8+4i+(-6)-i \xlongequal{ } \\[1 em] & \xlongequal{ }8+4i-6-i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3i+2\end{aligned} $$ | |
| ① | $$ 2i^2 = 2 \cdot (-1) = -2 $$$$ i^3 = \color{blue}{i^2} \cdot i =
( \color{blue}{-1}) \cdot i =
- \, i $$ |
| ② | $$ 3 \cdot -2 = -6 $$ |
| ③ | -i+i=0i-i+i=0i |
| ④ | Combine like terms: $$ \color{blue}{8} + \color{red}{4i} \color{blue}{-6} \color{red}{-i} = \color{red}{3i} + \color{blue}{2} $$ |
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