Answer
$$i(x(cosa+isina)-c)=ai^3nsx+aciosx-ci$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i(x(cosa+isina)-c)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}i(x(1acos+ai^2ns)-c) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}i(1acosx+ai^2nsx-c) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}aciosx+ai^3nsx-ci \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}ai^3nsx+aciosx-ci\end{aligned} $$ | |
| ① | $$ i s i n a = a i^{1 + 1} n s = a i^2 n s $$ |
| ② | Multiply $ \color{blue}{x} $ by $ \left( acos+ai^2ns\right) $ $$ \color{blue}{x} \cdot \left( acos+ai^2ns\right) = acosx+ai^2nsx $$ |
| ③ | Multiply $ \color{blue}{i} $ by $ \left( acosx+ai^2nsx-c\right) $ $$ \color{blue}{i} \cdot \left( acosx+ai^2nsx-c\right) = aciosx+ai^3nsx-ci $$ |
| ④ | Combine like terms: $$ ai^3nsx+aciosx-ci = ai^3nsx+aciosx-ci $$ |
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