Question
Answer
$$0.185e^{2t}-(0.092-j\cdot0.026)e^{-(3+j\cdot1.414)t}-(0.092+j\cdot0.026)e^{-(3-j\cdot1.414)t}=0.185e^{2t}-(0.092-0j)e^{-3t-jt}-(0.092+0j)e^{-3t+jt}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}0.185e^{2t}-(0.092-j\cdot0.026)e^{-(3+j\cdot1.414)t}-(0.092+j\cdot0.026)e^{-(3-j\cdot1.414)t}& \xlongequal{ }0.185e^{2t}-(0.092-0j)e^{-(3+j)t}-(0.092+0j)e^{-(3-j)t} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0.185e^{2t}-(0.092-0j)e^{-(3t+jt)}-(0.092+0j)e^{-(3t-jt)} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0.185e^{2t}-(0.092-0j)e^{-3t-jt}-(0.092+0j)e^{-3t+jt}\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{3+j}\right) \cdot t = 3t+jt $$$$ \left( \color{blue}{3-j}\right) \cdot t = 3t-jt $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(3t+jt \right) = -3t-jt $$Remove the parentheses by changing the sign of each term within them. $$ - \left(3t-jt \right) = -3t+jt $$ |
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