Answer
$$e^{ln\cdot2\cdot(3+i)}e^{ipi\cdot(3+i)}=e^{6ln+2iln}e^{3i^2p+i^3p}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}e^{ln\cdot2\cdot(3+i)}e^{ipi\cdot(3+i)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}e^{6ln+2iln}e^{i(3ip+i^2p)} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}e^{6ln+2iln}e^{3i^2p+i^3p}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2ln} $ by $ \left( 3+i\right) $ $$ \color{blue}{2ln} \cdot \left( 3+i\right) = 6ln+2iln $$Multiply $ \color{blue}{ip} $ by $ \left( 3+i\right) $ $$ \color{blue}{ip} \cdot \left( 3+i\right) = 3ip+i^2p $$ |
| ② | Multiply $ \color{blue}{i} $ by $ \left( 3ip+i^2p\right) $ $$ \color{blue}{i} \cdot \left( 3ip+i^2p\right) = 3i^2p+i^3p $$ |
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