Question
Answer
$$(3+2i)e\cdot2it+(3-2i)e-2it=4ei^2t+6eit-2ei-2it+3e$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+2i)e\cdot2it+(3-2i)e-2it& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3e+2ei)\cdot2it+3e-2ei-2it \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6e+4ei)it+3e-2ei-2it \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(6ei+4ei^2)t+3e-2ei-2it \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6eit+4ei^2t+3e-2ei-2it \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4ei^2t+6eit-2ei+3e-2it \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}4ei^2t+6eit-2ei-2it+3e\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{3+2i}\right) \cdot e = 3e+2ei $$$$ \left( \color{blue}{3-2i}\right) \cdot e = 3e-2ei $$ |
| ② | $$ \left( \color{blue}{3e+2ei}\right) \cdot 2 = 6e+4ei $$ |
| ③ | $$ \left( \color{blue}{6e+4ei}\right) \cdot i = 6ei+4ei^2 $$ |
| ④ | $$ \left( \color{blue}{6ei+4ei^2}\right) \cdot t = 6eit+4ei^2t $$ |
| ⑤ | Combine like terms: $$ 6eit+4ei^2t+3e-2ei = 4ei^2t+6eit-2ei+3e $$ |
| ⑥ | Combine like terms: $$ 4ei^2t+6eit-2ei-2it+3e = 4ei^2t+6eit-2ei-2it+3e $$ |
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