Question
Answer
$$(a+jb)xy+(a-jb)xz=bjxy-bjxz+axy+axz$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+jb)xy+(a-jb)xz& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1ax+bjx)y+(1ax-bjx)z \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}axy+bjxy+axz-bjxz \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}bjxy-bjxz+axy+axz\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{a+bj}\right) \cdot x = ax+bjx $$$$ \left( \color{blue}{a-bj}\right) \cdot x = ax-bjx $$ |
| ② | $$ \left( \color{blue}{ax+bjx}\right) \cdot y = axy+bjxy $$$$ \left( \color{blue}{ax-bjx}\right) \cdot z = axz-bjxz $$ |
| ③ | Combine like terms: $$ axy+bjxy+axz-bjxz = bjxy-bjxz+axy+axz $$ |
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