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