Question
Answer
$$\dfrac{-a+i\cdot(1-b)}{a+i\cdot(-1-b)}=\dfrac{-bi-a+i}{-bi+a-i}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-a+i\cdot(1-b)}{a+i\cdot(-1-b)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-a+i-bi}{a-i-bi} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-bi-a+i}{-bi+a-i}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{i} $ by $ \left( 1-b\right) $ $$ \color{blue}{i} \cdot \left( 1-b\right) = i-bi $$ |
| ② | Multiply $ \color{blue}{i} $ by $ \left( -1-b\right) $ $$ \color{blue}{i} \cdot \left( -1-b\right) = -i-bi $$ |
| ③ | Combine like terms: $$ -a+i-bi = -bi-a+i $$ |
| ④ | Combine like terms: $$ a-i-bi = -bi+a-i $$ |
This page was created using
Complex Expression calculator