Question
Answer
$$(x+iy)cosh(x+iy)=chi^2osy^2+2chiosxy+chosx^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+iy)cosh(x+iy)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1cx+ciy)osh(x+iy) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1cox+cioy)sh(x+iy) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(1cosx+ciosy)h(x+iy) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(1chosx+chiosy)(x+iy) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}chosx^2+chiosxy+chiosxy+chi^2osy^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}chi^2osy^2+2chiosxy+chosx^2\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{x+iy}\right) \cdot c = cx+ciy $$ |
| ② | $$ \left( \color{blue}{cx+ciy}\right) \cdot o = cox+cioy $$ |
| ③ | $$ \left( \color{blue}{cox+cioy}\right) \cdot s = cosx+ciosy $$ |
| ④ | $$ \left( \color{blue}{cosx+ciosy}\right) \cdot h = chosx+chiosy $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{chosx+chiosy}\right) $ by each term in $ \left( x+iy\right) $. $$ \left( \color{blue}{chosx+chiosy}\right) \cdot \left( x+iy\right) = chosx^2+chiosxy+chiosxy+chi^2osy^2 $$ |
| ⑥ | Combine like terms: $$ chosx^2+ \color{blue}{chiosxy} + \color{blue}{chiosxy} +chi^2osy^2 = chi^2osy^2+ \color{blue}{2chiosxy} +chosx^2 $$ |
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