Question
Answer
$$12i^{106}+2i^{79}+5i^6-6i^{87}=4i-17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}12i^{106}+2i^{79}+5i^6-6i^{87}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-12-2i-5+6i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4i-17\end{aligned} $$ | |
| ① | $$ 12i^{106} = 12 \cdot i^{4 \cdot 26 + 2} =
12 \cdot \left( i^4 \right)^{ 26 } \cdot i^2 =
12 \cdot 1^{ 26 } \cdot (-1) =
12 \cdot -1 = -12 $$ |
| ② | $$ 2i^{79} = 2 \cdot i^{4 \cdot 19 + 3} =
2 \cdot \left( i^4 \right)^{ 19 } \cdot i^3 =
2 \cdot 1^{ 19 } \cdot (-i) =
2 \cdot -i = -2i $$ |
| ③ | $$ 5i^6 = 5 \cdot i^{4 \cdot 1 + 2} =
5 \cdot \left( i^4 \right)^{ 1 } \cdot i^2 =
5 \cdot 1^{ 1 } \cdot (-1) =
5 \cdot -1 = -5 $$ |
| ④ | $$ -6i^{87} = -6 \cdot i^{4 \cdot 21 + 3} =
-6 \cdot \left( i^4 \right)^{ 21 } \cdot i^3 =
-6 \cdot 1^{ 21 } \cdot (-i) =
-6 \cdot -i = 6i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-2i} + \color{blue}{6i} \color{red}{-5} \color{red}{-12} = \color{blue}{4i} \color{red}{-17} $$ |
This page was created using
Complex Expression calculator