Question
Answer
$$6i^{14}-7i^{27}=7i-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6i^{14}-7i^{27}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-6+7i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7i-6\end{aligned} $$ | |
| ① | $$ 6i^{14} = 6 \cdot i^{4 \cdot 3 + 2} =
6 \cdot \left( i^4 \right)^{ 3 } \cdot i^2 =
6 \cdot 1^{ 3 } \cdot (-1) =
6 \cdot -1 = -6 $$ |
| ② | $$ -7i^{27} = -7 \cdot i^{4 \cdot 6 + 3} =
-7 \cdot \left( i^4 \right)^{ 6 } \cdot i^3 =
-7 \cdot 1^{ 6 } \cdot (-i) =
-7 \cdot -i = 7i $$ |
| ③ | Combine like terms: $$ 7i-6 = 7i-6 $$ |
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