Answer
$$cos(x+t\cdot(2+5i))+sin(x+t\cdot(2+5i))i=5i^3nst+5ciost+2i^2nst+i^2nsx+2cost+cosx$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}cos(x+t\cdot(2+5i))+sin(x+t\cdot(2+5i))i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}cos(x+2t+5it)+sin(x+2t+5it)i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}cos(5it+2t+x)+sin(5it+2t+x)i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5ciost+2cost+cosx+(5i^2nst+2inst+insx)i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5ciost+2cost+cosx+5i^3nst+2i^2nst+i^2nsx \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5i^3nst+5ciost+2i^2nst+i^2nsx+2cost+cosx\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{t} $ by $ \left( 2+5i\right) $ $$ \color{blue}{t} \cdot \left( 2+5i\right) = 2t+5it $$Multiply $ \color{blue}{t} $ by $ \left( 2+5i\right) $ $$ \color{blue}{t} \cdot \left( 2+5i\right) = 2t+5it $$ |
| ② | Combine like terms: $$ x+2t+5it = 5it+2t+x $$Combine like terms: $$ x+2t+5it = 5it+2t+x $$ |
| ③ | Multiply $ \color{blue}{cos} $ by $ \left( 5it+2t+x\right) $ $$ \color{blue}{cos} \cdot \left( 5it+2t+x\right) = 5ciost+2cost+cosx $$Multiply $ \color{blue}{ins} $ by $ \left( 5it+2t+x\right) $ $$ \color{blue}{ins} \cdot \left( 5it+2t+x\right) = 5i^2nst+2inst+insx $$ |
| ④ | $$ \left( \color{blue}{5i^2nst+2inst+insx}\right) \cdot i = 5i^3nst+2i^2nst+i^2nsx $$ |
| ⑤ | Combine like terms: $$ 5ciost+2cost+cosx+5i^3nst+2i^2nst+i^2nsx = 5i^3nst+5ciost+2i^2nst+i^2nsx+2cost+cosx $$ |
This page was created using
Complex Expression calculator